Correct.
"Stayin' Alive" by the Bee Gees was followed by "(Love Is) Thicker Than Water" by Andy Gibb, "Night Fever" by the Bee Gees and "If I Can't Have You" by Yvonne Elliman. "(Love Is) Thicker Than Water" was written with Andy, the other three with the other Bee Gees, Robin and Maurice.
Additionally, from December 1977 to September 1978, for 27 weeks out of 37, the US number one was written by Barry Gibb - before the four above was "How Deep Is Your Love" by the Bee Gees and later came "Shadow Dancing" by Andy Gibb and "Grease" by Frankie Valli.