The effect of the Coriolis force on the onset of the Benard-Marangoni convective instability in a horizontal fluid layer, subject to a rotation, is investigated. The upper surface is deformably free and the lower surface is bounded with a solid plate, heated from below. The principle of exchange of stability is applied. The characteristic problem is solved numerically, using the Runge-Kutta-Gill’s shooting method. The numerical results obtained compared Very well with previously published ones. The thickness ratio d(r), conductivity ratio k(r), Blot number Bi, Crispation number C and Taylor number Ta are significant on determining the critical Rayleigh number R(c) or Marangoni number M(c) with the corresponding critical wavenumber a(c). The results show that the system is more stabilizing at larger values of the thickness ratio d(r), conductivity ratio k(r), Riot number Ri and Taylor number Ta.