  We consider the branching ratio for the process $t \to c \gamma$ in the
context of the General Two Higgs Doublet Model type III. We find that taking
into account reasonable values for the parameter $\tan \beta$ is possible to
get values of this branching ratio up to orders of magnitude lying in the range
of sensitivity of near future top quark experiments. For values of $B(t \to c
\gamma) \sim 1-9 \times 10^{-5}$, values between 8-15 for $\tan \beta$ are
allowed.
