Context : Kepler observations revealed a brown dwarf eclipsing the M-type star LHSÂ 6343Â A with a period of 12.71Â days .
In addition , an out-of-eclipse light modulation with the same period and a relative semi-amplitude of \sim 2 \times 10 ^ { -4 } was observed showing an almost constant phase lag to the eclipses produced by the brown dwarf .
In a previous work , we concluded that this was due to the light modulation induced by photospheric active regions in LHSÂ 6343Â A .

Aims : In the present work , we prove that most of the out-of-eclipse light modulation is caused by the Doppler-beaming induced by the orbital motion of the primary star .

Methods : We introduce a model of the Doppler-beaming for an eccentric orbit and also considered the ellipsoidal effect .
The data were fitted using a Bayesian approach implemented through a Monte Carlo Markov chain method .
Model residuals were analysed by searching for periodicities using a Lomb-Scargle periodogram .

Results : For the first seven quarters of Kepler observations and the orbit previously derived from the radial velocity measurements , we show that the light modulation of the system outside eclipses is dominated by the Doppler-beaming effect .
A period search performed on the residuals shows a significant periodicity of 42.5 \pm 3.2 Â days with a false-alarm probability of 5 \times 10 ^ { -4 } , probably associated with the rotational modulation of the primary component .

Conclusions :