  A numerical method based on the transfer matrix method is developed to
calculate the critical temperature of two-layer Ising ferromagnet with a weak
inter-layer coupling. The reduced internal energy per site has been accurately
calculated for symmetric ferromagnetic case, with the nearest neighbor coupling
K1 = K2 = K (where K1 and K2 are the nearest neighbor interaction in the first
and second layers, respectively) with inter layer coupling J. The critical
temperature as a function of the inter-layer coupling J/K << 1, is obtained for
very weak inter-layer interactions,J/K < 0.1 . Also a different function is
given for the case of the strong inter-layer interactions (J/K > 1). The
importance of these relations is due to the fact that there is no well
tabulated data for the critical points versus J/K. We find the value of the
shift exponent Phi = Gama is 1.74 for the system with the same intra-layer
interaction and 0.5 for the system with different intra-layer interactions.
