Narendra and Balakrishnan proposed a way to construct a common quadratic Lyapunov function (CQLF), when a set of stable matrices are commutative. The purpose of this paper is to generalize the method to non-commutative and non-solvable case. A modified constructing algorithm is proposed and certain conditions are provided to assure the resulting matrix being a CQLF. Next, the problem discussed is when a stable matrix can be added to a set of matrices with CQLF to construct a new CQLF for the enlarged set. Narendra and Balakrishnan proposed a way to construct a common quadratic Lyapunov function (CQLF), when a set of stable matrices are commutative. The purpose of this paper is to generalize the method to non-commutative and non-solvable case. A modified constructing algorithm is proposed and certain conditions are provided to assure the resulting matrix being a CQLF. Next, the problem discussed is when a stable matrix can be added to a set of matrices with CQLF to construct a new CQLF for the enlarged set.