Summary: We describe the \(\omega\)-limit sets of all points of the square \(I^2:= [0,1]^2\) for a triangular map (skew product) given by S. Kolyada [Ergodic Theory Dyn. Syst. 12, No. 4, 749–768 (1992; Zbl 0784.58038)]. We prove for such a map the following uniform property: all points of \(I^2\) except those of the fiber \(I_0:= \{0\}\times [0,1]\), which are fixed points, have as infinity \(\omega\)-limit set the fiber \(I_0\).