Within the framework of the l0 regularized least squares problem, we focus, in this paper, on nonconvex continuous penalties to approximate the l0-norm which usually lead to better results than the l1 convex relaxation since they are more "l0-like". Based on some results in one dimension and in the orthogonal case, we propose the Continuous Exact l0 penalty (CEL0) leading to a relaxation of the l2 − l0 problem. Global minimizers of the objective function using CEL0 are proved to be the same as for the l2 − l0 problem in a given sense. We also demonstrate that all local minimizers of this functional are local minimizers for l2 − l0. However, the reciprocal is false and some local minimizers of the initial functional are not critical points for the relaxed one. Then solving the initial l2 − l0 problem is equivalent, in a sense, to solve it by replacing the l0-norm with the CEL0 penalty which provides better properties for the objective function although the problem remains nonconvex. Finally, recent nonsmooth nonconvex algorithms are used to address this relaxed problem within a macro algorithm ensuring the convergence to a critical point of the relaxed functional which is also a (local) optimum of the initial problem.