The dynamics of Bknard-Marangoni convection with unidimensional heating in a pure fluid is studied experimentally. Convection begins with rolls parallel to the heater. The characteristics of these primary rolls have been determined. When the temperature difference across the liquid layer is increased beyond a critical value a secondary instability appears. Motions transverse to the heater with a definite wavelength can be seen. Moreover, for small angles between the heater and the fluid surface, the pattern drifts along the heater with a velocity that depends almost linearly on the inclination. A phenomenological phase equation is proposed to interpret this observation.