  We have extended the enumeration of self-avoiding walks on the Manhattan
lattice from 28 to 53 steps and for self-avoiding polygons from 48 to 84 steps.
Analysis of this data suggests that the walk generating function exponent gamma
= 1.3385 +- 0.003, which is different from the corresponding exponent on the
square, triangular and honeycomb lattices. This provides numerical support for
an argument recently advanced by Cardy, to the effect that excluding walks with
parallel nearest-neighbour steps should cause a change in the exponent gamma.
The lattice topology of the Manhattan lattice precludes such parallel steps.
