This paper deals with the separation problem of dependent sources. The separation is made possible thanks to side information on the dependence nature of the considered sources. In this work, we first show how this side information can be used to achieve desired source separation using joint matrix decomposition techniques. Indeed, in the case of statistically independent sources, many BSS methods are based on joint matrix diagonalization. In our case, we replace the target diagonal structure by appropriate non diagonal one which reflects the dependence nature of the sources. This new concept is illustrated with two simple 2 2 source separation examples where second-order-statistics and high order-statistics are used respectively.