Abstract: Given a monic univariate polynomail $f\in \mathbb{F}_q[x]$. there are simple and well known algorithms for determining its square-free part. Assuming that $f(x)$ is a monic square-free polynomial of degree $n$, I will present a Berlekamp's algorithm for determining its complete factorization $f=f_1^{e_1}\dots f_k^{e_k}$, where $f_1,\dots, f_k$ are pairwise distinct monic irreducible polynomials and $e_1,\dots, e_k$ are positive integers.