A proper edge t-coloring of an undirected, simple, finite, connected graph G is a coloring of its edges with colors 1, 2, ..., t such that all colors are used, and no two adjacent edges receive the same color. A cyclically-interval t-coloring of a graph G is a proper edge t-coloring of G such that for each its vertex x at least one of the following two conditions holds: a) the set of colors used on edges incident to x is an interval of integers, b) the set of colors not used on edges incident to x is an interval of integers. For any positive integer t, let Mt be the set of graphs for which there exists a cyclically-interval t-coloring. Examples of bipartite graphs that do not belong to the class U t≥1 Mt are constructed.