  In this paper we study an evolution equation involving the normalized
$p$-Laplacian and a bounded continuous source term. The normalized
$p$-Laplacian is in non divergence form and arises for example from stochastic
tug-of-war games with noise. We prove local $C^{\alpha, \frac{\alpha}{2}}$
regularity for the spatial gradient of the viscosity solutions. The proof is
based on an improvement of flatness and proceeds by iteration.
