Abstract: Symmetry method is modern method in seeking conserved quantity. The form invariance is a new symmetry. The form invariance of differential equations of motion for generalized mechanical system in terms of quasi-coordinates is studied, under the infinitesimal transformations of groups. First, the definition and criterion of the form invariance are given. Next, the condition under which the invariance can lead to a conserved quantity is established. Finally, we give an example to illustrate the application of...