In this paper we consider the Krylov subspace based method introduced in [Fasano, 2005a], for iteratively solving the symmetric and possibly indefinite linear system Ax = b. We emphasize the application of the latter method to compute a diagonal preconditioner. The approach proposed is based on the approximate computation of the `2-norm of the rows (columns) of the matrix A and on its use to equilibrate the matrix A. The distinguishing feature of this approach is that the computation of the `2-norm is performed without requiring the knowledge of the entries of the matrix A but only using a routine which provides the product of A times a vector.