For a continuous selfmap $f$ of a compact metric space $X$ we study the set of its continuous extensions $F$ on the space $X\times I$, where $I$ is a compact interval. In particular, we have solved an open problem (raised in [Ll. Alseda, S. Kolyada, J. Llibre, and L. Snoha, Entropy and periodic points for transitive maps, Trans. Amer. Math. Soc. 351 (1999)]) by proving that any continuous transitive map $f$ on $X$ can be extended to a continuous transitive triangular map $F=(f,g_x)$ on $X\times I$ without increasing topological entropy.