  The branching theorem expresses irreducible character values for the
symmetric group $S_n$ in terms of those for $S_{n-1}$, but it gives the values
only at elements of $S_n$ having a fixed point. We extend the theorem by
providing a recursion formula that handles the remaining cases. It expresses
these character values in terms of values for $S_{n-1}$ together with values
for $S_n$ that are already known in the recursive process. This provides an
alternative to the Murnaghan-Nakayama formula.
