Summary: The aim of the present paper is to describe completely the dynamics of a triangular map \(F\) introduced by S. Kolyada [Ergodic Theory Dyn. Syst. 12, No. 4, 749–768 (1992; Zbl 0784.58038)] complementing the results given in [F. Balibrea, J. L. García Guirao and J. I. Muñoz Casado, Far East J. Dyn. Syst. 3, No. 1, 87–101 (2001; Zbl 1132.37313)]. We prove on one hand that there is no approxiamtely periodic points which are not fixed and on other hand that each pair of distinc points \(\{x, y\} \in I^2\setminus I_0\) is an asymptotic pair under the iteration of \(F\).