In this article we present the case of HD41004 AB, a system composed of a K0V star and a 3.7-mag fainter M-dwarf companion. We have obtained 86 CORALIE spectra of this system with the goal of obtaining precise radial-velocity measurements. Since HD41004 A and B are separated by only 0.5", in every spectrum taken for the radial-velocity measurement, we are observing the blended spectra of the two stars. An analysis of the measurements has revealed a velocity variation with an amplitude of about 50 m s(-1) and a periodicity of 1.3 days. This radial-velocity signal is consistent with the expected variation induced by the presence of a companion to either HD41004 A or HD41004 B, or to some other effect due to e.g. activity related phenomena. In particular, such a small velocity amplitude could be the signature of the presence of a very low mass giant planetary companion to HD41004 A, whose light dominates the spectra. The radial-velocity measurements were then complemented with a photometric campaign and with the analysis of the bisector of the CORALIE Cross-Correlation Function (CCF). While the former revealed no significant variations within the observational precision of similar to0.003-0.004 mag (except for an observed flare event), the bisector analysis showed that the line profiles are varying in phase with the radial-velocity. This latter result, complemented with a series of simulations, has shown that we can explain the observations by considering that HD41004 B has a brown-dwarf companion orbiting with the observed 1.3-day period. As the spectrum of the fainter HD41004 B "moves" relative to the one of HD41004 A (with an amplitude of a few km s(-1)), the relative position of the spectral lines of the two spectra changes, thus changing the blended line-profiles. This variation is large enough to explain the observed radial-velocity and bisector variations, and is compatible with the absence of any photometric signal. If confirmed, this detection represents the first discovery of a brown dwarf in a very short period (1.3-day) orbit around an M dwarf. Finally, this case should be taken as a serious warning about the importance of analyzing the bisector when looking for planets using radial-velocity techniques.
