We describe a new type of coronagraph, based on the principle of a phase mask as proposed by Roddier and Roddier a few years ago but using an original mask design found by one of us (D. R.), a four-quadrant binary phase mask (0, n) covering the full Ðeld of view at the focal plane. The mutually destructive interferences of the coherent light from the main source produce a very efficient nulling. The computed rejection rate of this coronagraph appears to be very high since, when perfectly aligned and phase-error free, it could in principle reduce the total amount of light from the bright source by a factor of 108, corresponding to a gain of 20 mag in brightness at the location of the Ðrst Airy ring, relative to the Airy peak. In the real world the gain is of course reduced by a strong factor, but nulling is still performing quite well, provided that the perturbation of the phase, for instance, due to the EarthÏs atmosphere, is efficiently corrected by adaptive optics. We show from simulations that a detection at a contrast of 10 mag between a star and a faint companion is achievable in excellent conditions, while 8 mag appears routinely feasible. This coronagraph appears less sensitive to atmospheric turbulence and has a larger dynamic range than other recently proposed nulling techniques : the phase-mask coronagraph (by Roddier and Roddier) or the Achromatic Interfero-Coronagraph (by Gay and Rabbia). We present the principle of the four-quadrant coronagraph and results of a Ðrst series of simulations. We compare those results with theoretical performances of other devices. We brieÑy analyze the di†erent limitations in space or ground-based observations, as well as the issue of manufacturing the device. We also discuss several ways to improve the detection of a faint companion around a bright object. We conclude that, with respect to previous techniques, an instrument equipped with this coronagraph should have better performance and even enable the imaging of extrasolar giant planets at a young stage, when coupled with additional cleaning techniques.