An efficient algorithm is presented for robust whitening in the presence of temporally uncorrelated additive noise that may be spatially correlated. This whitening is introduced as a pre-processing step in the blind source separation process. The robust whitening consists in the eigenvalue decomposition of a positive definite linear combination of a set a correlation matrices taken at nonzero lags. The coefficients of the linear combination are computed by a finite step global convergence algorithm. Some numerical simulations are provided to illustrate the effectiveness of the solution.