A multi-microphone hands-free device operating in noisy surroundings implements a method of de-noising a noisy sound signal. The noisy sound signal comprises a useful speech component coming from a directional speech source and an unwanted noise component, the noise component itself including a lateral noise component that is non-steady and directional. The method operates in the frequency domain and comprises combining signals into a noisy combined signal, estimating a pseudo-steady noise component, calculating a probability of transients being present in the noisy combined signal, estimating a main arrival direction of transients, calculating a probability of speech being present on the basis of a three-dimensional spatial criterion suitable for discriminating amongst the transients between useful speech and lateral noise, and selectively reducing noise by applying a variable gain specific to each frequency band and to each time frame.