The mostly used mathematical formulation of the inverse problem in electrocardiography is based on a least method using a transfer matrix that maps the electrical potential on the heart to the body surface potential (BSP). This mathematical model is ill based and a lot of works have been concentrating on the regularization term without thinking of reformulating the problem itself. We propose in this study to solve the inverse problem based on a domain decomposition technique on a fictitious mirror-like boundary conditions. We conduct BSP simulations to produce synthetic data and use it to evaluate the accuracy of the inverse problem solution.