We address the problem of blind source separation in the underdetermined and instantaneous mixture case. The proposed method is based on an algorithm developed by Aissa-El-Bey and al.. This algorithm requires a good choice of the noise threshold and does not take into account the noise contribution in the inversion process. In order to overcome these drawbacks, this paper presents a robust underdetermined blind source separation approach. Robustness is achieved by estimating the noise standard deviation and using this estimate in the inversion process and the expression of the noise threshold. The good performance of the proposed method is shown by comparison with state-of-the-art methods.