A new relation between the Lagranian and the first integral of a mechanical system was presented. On the basis of the relation, a new direct method to solve the inverse problem of the calculus of variations was given. It is proved that a first integral of differential equations with modified factors can be constructed a Lagrangian of the system. The partial differential equations to determine the modified factors were obtained. The new method was used to construct the Lagrangians and the families of Lagrangians of some different systems. The characteristics of the new solution were disscused.