  We show that the reduced Khovanov homology of a link $L$ in $S^3$ can be
expressed as the homology of a chain complex constructed from a description of
$L$ as the closure of a 1-tangle diagram in the annulus. The chain complex is
constructed using a resolution of the 1-tangle diagram into planar tangles in a
manner analogous to ordinary reduced Khovanov homology, but with some novel
features. In particular, unlike for ordinary Khovanov homology, terms appear in
the differential that are products of linear maps corresponding to pairs of
saddles obtained from the resolution. We also use the chain complex to
construct a spectral sequence that converges to reduced Khovanov homology.
