The paper deals with studying the domain decomposition algorithm with overlapping subdomains. This algorithm is based on the splitting method and uses the additive presentation of some bilinear form. Earlier this method was described for two subdomains. In our consideration we formulate the decomposition algorithm for an arbitrary number of subdomains and give the error estimation in L2-norm. The obtaning of this estimation is based on the analysis of the greed Green function of the implicit scheme operator. The method formulation is given in projection form with the finite element approximation. The approximate computation of the mass matrix is important in this paper. The lumping operators technique is used for this purpose. The results of this investigation were published earlier in Russian. For briefness we give some statements without proofs.