opinion: Justice Kennedy
  delivered the opinion of the Court.
  Like the shifting river channel near the property in dispute, this litigation has traversed from one side of our docket to the other. We must first recount this procedural history.
  In an earlier action, Mississippi citizens sued in the United States District Court for the Southern District of Mississippi to quiet title to the subject property. Certain Louisiana citizens were named as defendants. The parties asserted conflicting ownership claims to an area of about 2,000 acres, stretching seven miles along the Louisiana bank of the Mississippi River, near Lake Providence, Louisiana. The State of Louisiana and the Lake Providence Port Commission intervened in that action and filed a third-party complaint against the State of Mississippi. Concerned, however, with the jurisdiction of the District Court to hear its matter, Louisiana took the further step of instituting an original action in this Court, and it filed a motion here for leave to file a bill of complaint. We denied the motion. Louisiana v. Mississippi, 488 U. S. 990 (1988).
  The District Court heard the case pending before it and, in an order by Judge Barbour, ruled in favor of Mississippi. Louisiana, however, prevailed in the United States Court of Appeals for the Fifth Circuit, 937 F. 2d 247 (1991), and we granted Mississippi’s petition for certiorari. 503 U. S. 935 (1992).
  After hearing oral argument on both substantive issues and jurisdiction, we resolved only the latter. We held that there was no jurisdiction in the District Court, or in the Court of Appeals, to grant any relief in the quiet title action to one State against the other, that authority being reserved for jurisdiction exclusive to this Court. Mississippi v. Louisiana, 506 U. S. 73, 77-78 (1992); see also 28 U. S. C. § 1251(a). We remanded the case so the complaint filed by Louisiana could be dismissed in the District Court and for the Court of Appeals to determine what further proceedings were necessary with respect to the claims of the private parties.
  Upon remand, Louisiana asked the District Court to stay further action in the case to allow Louisiana once again to seek permission to file a bill of complaint in this Court. The District Court agreed, noting that our decision on the boundary issue would solve the District Court’s choice-of-law problem and would be the fairest method of resolving the fundamental issue for all parties.
  Louisiana did file a renewed motion in our Court for leave to file a bill of complaint. We granted it, allowing leave to file against Mississippi and persons called the Houston Group, who asserted ownership to the disputed area and who supported Mississippi’s position on the boundary issue. Louisiana asked us to define the boundary between the two States and cancel the Houston Group’s claim of title. After granting leave to file, we appointed Vincent L. McKusick, former Chief Justice of the Maine Supreme Judicial Court, as Special Master. The case is now before us on Louisiana’s exceptions to his report, and there is no jurisdictional bar to our resolving the questions presented.
  We deem it necessary to do no more than give a brief summary of the law and of the Special Master’s careful and well-documented findings and conclusions, for Louisiana’s exceptions have little merit and must be rejected.
  The controlling legal principles are not in dispute. In all four of the prior cases that have involved the Mississippi River boundary between Louisiana and Mississippi, we have applied the rule of the thalweg. Louisiana v. Mississippi, 466 U. S. 96, 99 (1984); Louisiana v. Mississippi, 384 U. S. 24, 25-26, reh’g denied, 384 U. S. 958 (1966); Louisiana v. Mississippi, 282 U. S. 458, 459 (1931); Louisiana v. Mississippi, 202 U. S. 1, 49 (1906). Though there are exceptions, the rule is that the river boundary between States lies along the main downstream navigational channel, or thalweg, and moves as the channel changes with the gradual processes of erosion and accretion. Louisiana v. Mississippi, 466 U. S., at 99-101; Arkansas v. Tennessee, 397 U. S. 88, 89-90 (1970). There exists an island exception to the general rule, which provides that if there is a divided river flow around an island, a boundary once established on one side of the island remains there, even though the main downstream navigation channel shifts to the island’s other side. Indiana v. Kentucky, 136 U. S. 479,508-509 (1890); Missouri v. Kentucky, 11 Wall. 395, 401 (1871). The island exception serves to avoid disturbing a State’s sovereignty over an island if there are changes in the main navigation channel.
  The Special Master found that the disputed area derived from an island, known as Stack Island, that had been within Mississippi’s boundary before the river’s main navigational channel shifted to the east of the island. The Special Master found that, through erosion on its east bank and accretion on its west bank, Stack Island changed from its original location, next to the Mississippi bank of the river, to its current location, abutting the Louisiana bank. Pursuant to the island exception, then, the Special Master placed the boundary on the west side of the disputed area, confirming Mississippi’s sovereignty over it. Because the land is located in Mississippi, the Special Master found that Louisiana had no standing to challenge the Houston Group’s claim of title.
  Louisiana advances a different version of events. It concedes that there did exist a Stack Island in 1881 and that it was formed in Mississippi territory. In that year the land was surveyed for a federal land patent that was later granted to the Houston Group’s predecessor in interest, Stephen Blackwell. Louisiana maintains that two years later, in 1883, Stack Island washed away and was replaced by mere alluvial deposits, which at various times over the last 100 years were not sufficient in size or stability to be deemed an island. Some of these alluvial deposits may or may not have gravitated to the disputed area; nonetheless, according to Louisiana, the disputed area was not formed from anything that can be said to be Stack Island but rather was formed by random accretion to the west bank of the river.
  The Special Master rejected Louisiana’s theory as not supported by the evidence, and we agree. The only evidence that Louisiana presented to support its theory of Stack Island’s disappearance is a Mississippi River Commission map dated April 1883. The map was prepared in 1881, with hy-drographic data added in an overlay in 1883. Of particular interest is a solid green line labeled as the “present steamboat channel” that runs over a portion of Stack Island as it was drawn in 1881. Louisiana’s expert interpreted that green line to mean that Stack Island had disappeared by 1883.
  The Special Master questioned the authenticity of the document because testimony suggested that no such map had been published by the Mississippi River Commission and because a different map published by the Commission the same month, April 1883, showed Stack Island in existence. Even if we assume the document’s authenticity, however, it does not settle the question, for we agree with the Special Master that boats could have passed close enough to the island without the entire island having disappeared. Louisiana’s reading of the document was contradicted, moreover, by the sworn testimony of Stephen Blackwell and two other witnesses given on May 5, 1885, stating that Blackwell and his family had lived on Stack Island continuously from April 2, 1882, to the date of the testimony and were cultivating 20 acres. Furthermore, in November 1883, six months after Stack Island was supposed to have vanished, the Mississippi River Commission, in reporting on its construction of dikes just north of Stack Island, stated that “ ‘this work showed good results, forcing the main channel of the river to the right of the island and building a bar to the head of Stack Island, as shown by the high-water survey of April 1883.’” Report of Special Master 20.
  Like the Special Master, we are unconvinced that Stack Island disappeared in 1883. Louisiana alleges other disappearances, including one as recently as 1948. We find no credible evidence of these disappearances, but instead find compelling evidence of Stack Island’s continued existence. We note first that the north portion of Stack Island has 70-year-old cottonwood trees growing on it and that long-time residents of the area report no disappearances of the island. The record, moreover, contains numerous maps of the region beginning with the 1881 patent survey and coming into the present era, and every one of them shows the existence of Stack Island. With the exception of a single exhibit, dated 1970, all of the maps and mosaics show a land mass that the mapmaker identifies by name as Stack Island, even for the years since 1954 when that land mass has no longer been insular in form. These maps show Stack Island’s progression from the Mississippi side of the river to the Louisiana side. When the maps are superimposed one over the other in chronological order, the successive maps show a land mass covering a significant portion of Stack Island shown on the preceding map. The maps satisfy us that Stack Island did not wash away and is now the disputed area.
  We need not delve into the proper definition of an island, as Louisiana would have us do, because the Special Master adopted Louisiana’s rigorous test, and found that Stack Island satisfied it.
  Louisiana raises no exceptions to that portion of the Special Master’s report finding that Louisiana lacked standing to challenge the Houston Group’s claim of title. Louisiana requests a new trial of the supplemental hearing before the Special Master but offers no sound reason in support of that request, so we must deny it.
  We have considered Louisiana’s other exceptions and find them insubstantial. The exceptions of Louisiana are overruled, and the Special Master’s report and proposed decree are adopted.
  It is so ordered.
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