We analyze the square lattice, which is allowed to fold on itself along its bonds in a two-dimensional embedding space, with bending energy (u) and attractive (\ensuremath{\omega}0) or repulsive (\ensuremath{\omega}g0) interactions. We discuss two types of interaction, the first one is proportional to the contact area and the second one is proportional to the number of pairs of elementary squares which occupy the same place in the plane. We obtain the phase diagrams in the (u,\ensuremath{\omega}) plane for both interactions. We also perform the numerical analysis for the first type of interaction and discuss its relation to the sequential folding transition of the polymerized membrane with the attractive interaction [F. F. Abraham and M. Kardar, Science 252, 419 (1991)]. \textcopyright{} 1996 The American Physical Society.