  An Ising model for damage spreading with a probability of damage healing ($q
= 1 - p$) is proposed and studied by means of Monte Carlo simulations. In the
limit $p \to 1$ the new model is mapped to the standard Ising model. It is
found that, for temperatures above the Onsager critical temperature ($T_{C}$),
there exist a no trivial finite value of $p$ that sets the critical point
($p_{c}$) for the onset of damage spreading. It is found that $p_{c}$ depends
on $T$, defining a critical curve at the border between damage spreading and
damage healing. Transitions along such curve are found to belong to the
universality class of directed percolation. The phase diagram of the model is
also evaluated showing that for large $T$ one has $p_{c} \propto (T-
T_{C})^{\alpha}$, with $\alpha = 1$. Within the phase where the damage remains
active, the stationary value of the damage depends lineally on both $p - p_{c}$
and $T - T_{C} $.
