A new geometric constant C ( )pz( ) X for a Banach space X is introduced ，called the generalizedZbaganu constant. Next，it is shown that the upper and the lower bounds of the constant estimation for any Banach space X. Moreover，it gives the equivalent conditions of X is uniformly non-square and that discusses the relationship between the James constant and C ( )pz( ) X . Finally，the relationship between C (p)z(X) and the fixed point property is found.