The CROSSING NUMBER cr(G) of a graph G is the minimum NUMBER of edge CROSSINGs over all drawings of G in the plane. In the paper, we extend known results concerning CROSSING NUMBERs of join products of two small graphs with cycles. The CROSSING NUMBER of the join product G∗ + Cn for the disconnected graph G∗ consisting of the complete graph K4 and one isolated vertex is given, where Cn is the cycle on n vertices. The proof of the main result is done with the help of lemma whose proof is based on a special redrawing technique. Up to now, the CROSSING NUMBERs of G + Cn are done only for a few disconnected graphs G. Finally, by adding new edge to the graph G∗, we are able to obtain the CROSSING NUMBER of G1 + Cn for one other graph G1 of order five.