Summary: The standard Schur complement equation-based implementation of interior-point methods for second order cone programming may encounter stability problems in the computation of search directions, and as a consequence, accurate approximate optimal solutions are sometimes not attainable. Based on the eigenvalue decomposition of the \((1,1)\) block of the augmented equation, a reduced augmented equation approach is proposed to ameliorate the stability problems. Numerical experiments show that the new approach can achieve more accurate approximate optimal solutions than the Schur complement equation-based approach.