In the existing literature, the interactions between the vortex ''pancakes'' believed to form in, e.g., Bi2Sr2CaCu2O8, have been attributed to a combination of magnetic and Josephson effects. Both these effects lead to an attraction between pancakes in neighboring CuO2 planes. We show that there exists a third mechanism of interaction, namely, the indirect effect of the Coulomb interaction, which leads to a repulsion between such pancakes. The relative strength of this coupling is estimated.