  We argue that the geometric discord introduced in [B. Dakic, V. Vedral, and
C. Brukner, Phys. Rev. Lett. 105, 190502 (2010)] is not a good measure for the
quantumness of correlations, as it can increase even under trivial local
reversible operations of the party whose classicality/non-classicality is not
tested. On the other hand it is known that the standard, mutual-information
based discord does not suffer this problem; a simplified proof of such a fact
is given.
