  A generalization of the geometric measure of quantum discord is introduced in
this article, based on Hellinger distance. Our definition has virtues of
computability and independence of local measurement. In addition it also does
not suffer from the recently raised critiques about quantum discord. The exact
result can be obtained for bipartite pure states with arbitrary levels, which
is completely determined by the Schmidt decomposition. For bipartite mixed
states the exact result can also be found for a special case. Furthermore the
generalization into multipartite case is direct. It is shown that it can be
evaluated exactly when the measured state is invariant under permutation or
translation. In addition the detection of quantum phase transition is also
discussed for Lipkin-Meshkov-Glick and Dicke model.
