  Geometric discord, a measure of quantumness of bipartite system, captures
minimal nonlocal effects of a quantum state due to locally invariant von
Neumann projective measurements. Original version of this measure is suffered
by the local ancilla problem. In this article, we propose a new version of
geometric discord using affinity. This quantity satisfies all criteria of a
good measure of quantum correlation of the bipartite system and resolves local
ancilla problem of Hilbert-Schmidt norm based discord. We evaluate analytically
the proposed quantity for both pure and mixed states. For an arbitrary pure
state, it is shown that affinity based geometric discord equal to geometric
measure of entanglement. Further, we obtain a lower bound of this measure for m
\times n dimensional arbitrary mixed state and a closed formula of proposed
version of geometric discord for 2 \times n dimensional mixed state is
obtained. Finally, as an illustration, we have studied the nonlocality of Bell
diagonal state, isotropic and Werner states.
