A new approach using the decomposition ofA(t) to study the commutative class of linear time-varying systems is presented. A simpler and computer-implemental criterion of checking the commutativity ofA(t) with its integral is given. More transparent results on solution, stability, decoupling, the controlability and observability are obtained. With the new approach, a commutative linear time-varying system can be studied in the same manner as that of a linear time-invariant system.