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<br> <br><p>A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance, which has virtue of computability and independence of local measurements. In addition our definition also does not suffer from the recently raised critiques about quantum discord. Importantly the exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition of the states. For bipartite mixed states the exact result can also be found for X𝑋Xitalic_X type case, of which the sub matrices are spanned by the Schmidt-typed states. Furthermore this definition has a natural generalization into multipartite states. As for symmetric case, permutational or translational invariance, we shown that it can be evaluated exactly by supposing that the ”nearest” completely classical state shares the same symmetry of the state. In addition we show th