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The orbital products of occupied and virtual orbitals are employed as an expansion basis for the charge density generating the local potential in the optimized effective potential method thus avoiding the use of auxiliary basis sets. The high computational cost arising from the quadratic increase of the dimension of this product basis with system size can be greatly reduced by elimination of the linearly dependent products according to a procedure suggested by Beebe and Linderberg [Int. J. Quantum Chem. 12, 683 (1977)]. Numerical results from this approach show a very good agreement with those obtained from balancing the auxiliary basis for the expansion of the local potential with the orbital basis set. [ABSTRACT FROM AUTHOR]