Abstract:The inverse problem of the calculus of variations for the firstorder system was restudied. The errors on the conditions of selfadjointness for a system of the firstorder ordinary differential equations in some literatures were amend. The equations to determine the matrices of the selfadoint transformations for the firstorder system were obtained. Two methods of constraction of the Lagrangians for the firstorder selfadjoint system were presented. An example was given to illustrate the application of the result.