When using the Pontryagin Maximum Principle in optimal control problems the most difficult part of the numerical solution is associated with the non-linear operation of the maximization of the Hamiltonian over the control variables. For a class of problems, the optimal control vector is a vector function with continuous time derivatives. A method is presented to find this smooth control without the maximization of Hamiltonian. Three illustrative examples are considered. (C) 2004 Elsevier Ltd. All rights reserved.