In the context of the narrow-band or wideband array processing problem, in this study a robust method is developed to improve the accuracy of the estimation of the direction-of-arrival of the sources. It is well known that when the noise cross-spectral matrix is unknown, these estimates may be grossly inaccurate. Using both a least-squares algorithm and a noneigenvector algorithm to estimate the noise subspace projection matrix and then its corresponding eigenvalues using the Rayleigh quotient, a new robust algorithm for the source characterization problem in the presence of noise with an unknown cross-spectral matrix is developed. It is shown that the performance of bearing estimation algorithms improves substantially when the robust estimate is used. Simulation results are presented for the Toeplitz band noise spectral matrix model.