A recently developed numerical method, based on the exact-diagonalization calculations, is used to study ground states of the two-dimensional Falicov-Kimball model (FKM) with correlated hopping (t') in the symmetric case. It is shown that the ground-state phase diagram as well as the picture of valence and metal-insulator transitions found for the conventional FKM (without correlated hopping) are strongly changed when the correlated hopping term is added. In particular, it was found that for intermediate t' and f level energy E-f < 0, the phases with noninteger valency are suppressed and the metallic phase disappears. On the other hand, for strong t', the metallic phase is stabilized for a wide region of model parameters. (c) 2005 Elsevier B.V. All rights reserved.