  A new quantum correlation in terms of the average distance between the
reduced state and the $i$-th output reduced states under local von Neumann
measurements is proposed. It is shown that only the product states do not
contain this quantum correlation and thus it is different from both the quantum
discord (QD) [Phys. Rev. Lett. \textbf{88}, 017901 (2001)] and the
measurement-induced nonlocality (MIN) [Phys. Rev. Lett. \textbf{106},
120401(2011)]. For pure states, it is twice of the quantity MIN, and is smaller
than QD and entanglement of formation (EOF). A general analytical formula is
given and a lower bound for the two qubits case is obtained. Furthermore, we
compare it with EOF and QD through the Werner state and the isotropic state
respectively.
