The register allocation in loops is generally carried out after or during the software pipelining process. This is because doing the register allocation at first step without assuming a schedule lacks the information of interferences between values live ranges. The register allocator introduces extra false dependencies which reduces dramatically the original ILP (Instruction Level Parallelism). In this paper, we give a new formulation to carry out the register allocation before the scheduling process, directly on the data dependence graph by inserting some anti dependencies arcs (reuse edges). This graph extension is first constrained by minimizing the critical cycle and hence minimizing the ILP loss due to the register pressure. The second constraint is to ensure that there is always a cyclic register allocation with the set of available registers, and this for any software pipelining of the new graph. We give the exact formulation of this problem with linear integer programming.