  A new algorithm for the derivation of low-density series for percolation on
directed lattices is introduced and applied to the square lattice bond and site
problems. Numerical evidence shows that the computational complexity grows
exponentially, but with a growth factor $\lambda < \protect{\sqrt[8]{2}}$,
which is much smaller than the growth factor $\lambda = \protect{\sqrt[4]{2}}$
of the previous best algorithm. For bond (site) percolation on the directed
square lattice the series has been extended to order 171 (158). Analysis of the
series yields sharper estimates of the critical points and exponents.
