We introduce a generalized concept of uniformly nonsquare which of course contains usual uniformly nonsquare, and a generalized Gao constant E(a, X). We give the relations between this definition and some generalized constants, including C(a, X), J (a, X), and E(a, X). We also give some properties of the generalized Gao constant E(a, X). Finally, we compute E(a, H) for Hilbert space and give some examples.