Given a set of clients and a set of potential sites for facilities, the p-median problem consists of opening a set of p sites and assigning each client to the closest open facility to it. In [Elloumi, S., A tighter formulation of the p-median problem, J. Comb. Optim., 19 (2004), 69?83], a new formulation of this problem was proposed that takes benefit from identical values in the distance matrix. This formulation, when directly used in a mixed integer linear programming software, was proved to perform better than other known formulations, on a large number of instances. Here, we propose to improve the performances of the new formulation by taking benefit from its structure in the solution of its LP-relaxation. Rows and columns are gradually added to the linear program until a condition on the optimal values of the variables is reached. A computational comparison is carried out on many classes of instances.