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The group of automorphisms of the Brandt $\lambda^0$-extension$B^0_\lambda(S)$ of an arbitrary monoid $S$ with zero is described. Inparticular we show that the group of automorphisms$\mathbf{Aut}(B_{\lambda}^0(S))$ of $B_{\lambda}^0(S)$ is isomorphic to ahomomorphic image of the group defines on the Cartesian product$\mathscr{S}_{\lambda}\times \mathbf{Aut}(S)\times H_1^{\lambda}$ with thefollowing binary operation: \begin{equation*}  [\varphi,h,u]\cdot[\varphi^{\prime},h^{\prime},u^{\prime}]=[\varphi\varphi^{\prime},hh^{\prime},\varphi u^{\prime}\cdot uh^{\prime}],\end{equation*} where $\mathscr{S}_{\lambda}$ is the group of all bijections ofthe cardinal $\lambda$, $\mathbf{Aut}(S)$ is the group of all automorphisms ofthe semigroup $S$ and $H_1^{\lambda}$ is the direct $\lambda$-power of thegroup of units $H_1$ of the monoid $S$.

On the group of automorphisms of the Brandt $\lambda^0$-extension of a monoid with zero