There are various results concerning the strong Markov property for one-dimensional processes. The essence of these results can be expressed as follows. For a «good» Markov process $x_t$ and a special class of random times $\tau$ (the so called optional times): a) the behaviour of the process $x_t$ before $\tau$ and its behaviour after $\tau$ are conditionally independent given $\tau$ , $x_{\tau}$ ; b) the forecast of the process' behaviour after $\tau$ based on known $\tau$ , $x_{\tau}$ is quite the same as if $\tau$ be non-random (this forecast is determined by the transition function $p(\tau,x_{\tau},s,\Gamma)$ ). Williams and Jacobsen introduced a class of random times$\tau$, the so called splitting times, for which property a) only is valid. In this paper, the concept of splitting time is generalized for random fields.A random field is defined as a system of$\sigma$-algebras$\{\mathscr F_V\}$,$V$being a closed subset of a finite-dimensional Euclidean space$X$. The Markov property means that$\mathscr F_V$and$\mathscr F_W$are conditionally independent given$\mathscr F_{V\bigcap W}$provided$V\bigcup W=X$. A random time is a pair of random closed sets$V$and$W$such that$V\bigcup W=X$. Given$\tau=(V,W)$, we introduce the$\sigma$-algebras of the «past»$\mathscr F_V$, the «future»$\mathscr F_W$and the «present»$\mathscr F_{V\bigcap W}$. A random time$\tau$is called a splitting time if the past and the future are conditionally independent given the present. We give necessary and sufficient conditions for a random time with countably many values to be splitting and find sufficient conditions in the case of uncountably many values.