In 1965–66 Corby progressed beyond the first round of the FA Cup for the first time; after beating non-League Burton Albion 6–3 in the first round, they won 1–0 at Luton Town in a second round replay after the first match ended 2–2. In the third round they were beaten 6–0 at Plymouth Argyle. The club applied for Football League membership for a fourth time, and for the first time received a single vote for their unsuccessful bid. The club made their final application in 1966–67, again receiving no votes. The following season saw another FA Cup first round appearance (a 1–0 defeat at Boston United) but ended in relegation to Division One. In 1971 the club were placed in Division One North after league reorganisation. Further reorganisation in 1979 and 1982 saw them placed in the Midland Division and then the Premier Division.