A nonNoether conserved quantity, i. e. Hojman conserved quantity constructed using the Noether symmetry for the nonholonomic mechanical system is presented. Under special infinitesimal transformations in which the time is not variable, the special Noether symmetry and Noether conserved quantity are given, and the condition under which the special Noether symmetry is a special Lie symmetry is obtained. From the special Noether symmetry, the Hojman conserved quantity of the corresponding holonomic system, the weakly Hojman conserved quantity and the strongly Hojman conserved quantity of the nonholonomic systems are obtained. An example is given to illustrate the application of the result.