Let $(X,\mathcal F,\mu,T)$ be an ergodic invertible measure-preserving system with a finite generating partition $\mathcal P$. If $\mathcal P$ is very weak Bernoulli, then $(X,\mathcal F,\mu,T)$ is isomorphic to a Bernoulli shift with entropy $h_\mu(T)=h_\mu(T,\mathcal P)$.