  From the very beginning the Khovanov homology appears to be one of the most
important invariant of knots; for computational and theoretical reasons it
would be useful to operate with reduced version of it - nevertheless the
definition given by Khovanov appears to be not natural in a sense that it
requires choices of circles in every resolution of knot diagram. We propose a
definition that generalizes the reduced odd Khovanov homology defined by
Rasmussen, Ozsvath and Szabo to the case of Putyra's chronological homology and
therefore gives a simple and natural way to reduce the standard Khovanov
homology. Surprisingly the construction works as well for virtual knots and
links.
