 He scored seven times in 28 matches in the 1957–58 season, as Palace finished in 14th place.He scored 17 goals in 45 matches in the 1958–59 season, in which the club became founder members of the Fourth Division and new manager George Smith led the "Glaziers" to a seventh-place finish.In 1959–60 Byrne scored 16 times in 42 matches as Palace finished eighth in Division Four.