Flag of the United States Secretary of the Navy.  It dates from at least 1865, and the version with four stars since at least 1867, remaining mostly unchanged since (though the anchor has gradually gotten bigger and been redesigned a bit).  It is defined in naval regulations, document NTP 13(B) [1] section 1806, as:
The flag of the Secretary of the Navy shall consist of a rectangular blue field with a fouled white anchor in the center. Four white stars flank the anchor, two on each side, all with one point of each star upward.  A gold fringe is authorized for use on the flag when it is displayed in a static, indoor position. The cord and tassels are of golden yellow.
For more information, see SeaFlags.
Self-made following photos of flags
Carl Lindberg