The onset of thermal stabilities of the horizontally superposed systems of fluid and porous layers, in a rotating coordinate, is investigated. Boussinesq’s approximation, local volume average technique and Darcy’s law are employed and the slipping interface is assumed. The top and bottom boundaries of the system are assumed rigid and isothermal. A Sturm-Liouville’s problem is derived and solved numerically. The critical Rayleigh number R(c) or R(mc) and wavenumber a(c) or a(mc) are obtained for various values of depth ratio (d) over cap thermal conductivity ratio k/k(m), permeability K, proportionality constant in the slip condition ti and Taylor number Ta. The sole effect of relation is stabilizing. The previous results with Ta = 0, using different methods, are compared very well.