<p>The finite-time anti-synchronisation in the mean-square sense of time-delayed Dirichlet boundary valued space-time discrete Markovian BAM neural networks is investigated in this paper. In this paper, we derive some results for the criteria of finite-time asymptotic anti-synchronization of BAM neural networks based on the Lyapunov–Krasovskii functional, the discrete inequality of the Wirtinger type and the discrete formula of integration by parts. Incorporating with the Lyapunov–Krasovskii functional involving the double sum of the delay-dependent component, finite-time exponential anti-synchronization is investigated for better showing the synchronized networks than asymptotic anti-synchronization. This study shows that the finite-time mean-squared anti-synchronisation of space-time discrete Markovian BAM neural networks can be better ensured with the smaller diffusion intensities, time delays and larger self-feedback connection weights. In comparison with the studies on global-time anti-synchronisation, the results of this paper, providing a framework to discuss the issue of finite-time anti-synchronisation for space-time discrete models of neural networks, have a wide range of applications. Finally, the validity of the method is verified by means of an illustrative example.</p>