  In this paper, we construct a canonical grading on bordered Heegaard Floer
homology by homotopy classes of nonvanishing vector fields. This grading is a
generalization of our construction of an absolute grading on Heegaard Floer
homology and it extends the well-known grading with values in a noncommutative
group defined by Lipshitz-Ozsv\'ath-Thurston.
