This paper addresses the robustness of adaptive narrowband beamforming with respect to bandwidth based on the loss of performance in terms of Signal to Interference plus Noise Ratio (SINR). The criterion used by Zatman to define narrowband environment, i.e. the ratio between the jammer plus noise covariance matrix and the noise eigenvalue, is studied from the point of view of a loss of SINR after narrowband beamforming under non narrowband conditions. Using theoretical results about the eigenvalues and eigenvectors of covariance matrices for signals closely spaced in frequency by Lee [5], it is shown that Zatman's criterion can be interpreted as an upper bound on the SINR loss which is nearly reached under certain conditions that are specified