  The effect of the surface coupling $J_s$ on the dependency of the layering
transition temperature $T_L$ as a function of the thickness $N$, of a spin-1/2
Ising film, is studied using the mean field theory. It is found that for $J_s$
greater than a critical value ($J_{sc}=1.30$), the layering transition
temperature decreases when the film thickness $N$ increases for any values of
the surface magnetic field $H_s$. While, for $J_s < J_{sc}$, the behaviour of
the layering transition temperature $T_L$, as a function of $N$, depends
strongly on the values of $H_s$. Indeed, we show the existence of three
distinct behaviours of $T_L$, as a function of the film thickness $N$,
separated by two critical surface magnetic fields $H_{sc1}$ and $H_{sc2}$,
namely: $(i)$ for $H_s < H_{sc1}$, $T_L$ increases with $N$; $(ii)$ for
$H_{sc1} < H_s < H_{sc2}$, $T_L$ increases for small values of $N$, and
decreases for large value ones; (iii) while for $H_s > H_{sc2}$, $T_L$
decreases with increasing the film thickness. Furthermore, depending on the
values of $J_s$, the wetting temperature $T_w (T_w=T_L$ when $N \to \infty$ for
a given material), can be greater or smaller than the layering transition
temperature of a film of thickness $N$ of the same material.
