  Given any diagram of a link, we define on the cube of Kauffman's states a
"2-complex" whose homology is an invariant of the associated framed links, and
such that the graded Euler characteristic reproduces the unnormalized Kauffman
bracket. This includes a categorification of brackets skein relation. Then we
incorporate the orientation information and get a further complex on the same
cube that gives rise to a new invariant homology for oriented links, so that
the graded Euler characteristic reproduces the unnormalized Jones polynomial in
Kauffman's version. Finally we clarify the relations between this homology and
the original Khovanov homology of oriented links, extending the well known
relation between the associated two versions of the Jones polynomial.
