In the present research work, a well known relation between mass (M), angular momentum (J) and spin parameter (a*) has established by entirely new mathematical operation using the model for first law of black hole mechanics given by the equation 8 kM δ δ A δ J υδ Q π = + Ω − (Bardeen et al. 1973) and the relation Ω = M / 2J .(Meinel, 2006), which concludes that the angular momentum may be regarded as additional characterizing parameter of black holes.