  We consider SDEs with bounded and $\alpha$-H\"older continuous drift, with
$\alpha \in (0,1)$, driven by multiplicative noise. We show that under
sufficient conditions on the diffusion matrix, which guarantee the existence of
a unique strong solution, the weak rate of convergence for the Euler-Maruyama
scheme is almost $(1+\alpha)/2$. The present paper forms part of the author's
master's thesis.
