  We study holomorphic maps between C$^*$-algebras $A$ and $B$. When $f:B_A
(0,\varrho) \longrightarrow B$ is a holomorphic mapping whose Taylor series at
zero is uniformly converging in some open unit ball $U=B_{A}(0,\delta)$ and we
assume that $f$ is orthogonality preserving on $A_{sa}\cap U$, orthogonally
additive on $U$ and $f(U)$ contains an invertible element in $B$, then there
exist a sequence $(h_n)$ in $B^{**}$ and Jordan $^*$-homomorphisms $\Theta,
\widetilde{\Theta} : M(A) \to B^{**}$ such that $$ f(x) = \sum_{n=1}^\infty h_n
\widetilde{\Theta} (a^n)= \sum_{n=1}^\infty {\Theta} (a^n) h_n,$$ uniformly in
$a\in U$. When $B$ is abelian the hypothesis of $B$ being unital and $f(U)\cap
\hbox{inv} (B) \neq \emptyset$ can be relaxed to get the same statement.
