  We describe a new method for combinatorially computing the transverse
invariant in knot Floer homology. Previous work of the authors and Stone used
braid diagrams to combinatorially compute knot Floer homology of braid
closures. However, that approach was unable to explicitly identify the
invariant of transverse links that naturally appears in braid diagrams. In this
paper, we improve the previous approach in order to compute the transverse
invariant. We define a new combinatorial complex that computes knot Floer
homology and identify the BRAID invariant of transverse knots and links in the
homology of this complex.
