The inverse problem of the calculus of variations for the firstorder system was restudied. The errors on the conditions of selfadjointness for a system of the firstorder ordinary differential equations in some literatures were amend. The equations to determine the matrices of the selfadoint transformations for the firstorder system were obtained. Two methods of constraction of the Lagrangians for the firstorder selfadjoint system were presented. An example was given to illustrate the application of the result.