This paper deals with a non-Noether conserved quantity constructed directly by u sing the form invariance for the Nielsen equation of a non-conservative mechanic al system. The definition and the criterion of a non-point form invariance of th e equation, of which the Noether conserved quantity is studied, are established by relying on the total time derivative along the trajectory of the equation. T he condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced, and three corollar ies in special cases are presented. Two examples are finally given to illustrate the application of the results.