This paper describes a method for solving the reserve constrained economic dispatch problem when some of the on-line generating units have prohibited operating zone(s). For a unit with prohibited zone(s), the zone(s) divide the operating region between the minimum generation limit (Pmin) and the maximum generation limit (Pmax) into disjoint convex sub-regions. These disjoint sub-regions form a non-convex decision space and the associated economic dispatch problem is thus a non-convex optimization problem. As a result, the conventional Lagrangian relaxation (LR) approach (e.g. the lambda-delta iterative approach) cannot be applied directly. The method proposed in this paper decomposes the non-convex decision space into a small number of subsets such that each of the associated dispatch problems is either infeasible or one that can be directly solved via the conventional LR approach. Based on the decomposition, the optimal solution is the least cost one among all the feasible solutions of the associated dispatch problems . In the paper examples are also given to illustrate the proposed method.