  We compute the first four coefficients of the asymptotic off-diagonal
expansion of the Bergman kernel for the N-th power of a positive line bundle on
a compact Kaehler manifold, and we show that the coefficient b_1 of the
N^{-1/2} term vanishes when we use a K-frame. We also show that all the
coefficients of the expansion are polynomials in the K-coordinates and the
covariant derivatives of the curvature and are homogeneous with respect to the
weight w.
