A search is conducted for a target moving in discrete time among a finite number of cells according to a known Markov process. The searcher must choose one cell in which to search in each time period. The set of cells from which he can choose is a function of the cell chosen in the previous time period. The problem is to find a searcher path, i.e., a sequence of search cells, that minimizes the probability of not detecting the target in a fixed number of time periods. The problem is formulated as a nonlinear program and solved for a local optimum by a simple implementation of the convex simplex method.