Facial reduction is a pre-processing method aimed at reformulating a problem to ensure strict feasibility. The importance of constructing a robust model is widely recognized in the literature, and facial reduction has emerged an attractive approach for achieving robustness. In this note, we outline a facial reduction algorithm for a standard spectrahedra, the intersection of the cone of positive semidefinite matrices and a set of linear equalities. We address an optimization problem that serves as an intermediate step in the facial reduction process. To tackle this optimization problem, we employ an interior point method that uses the Gauss-Newton method.