We present first results from calculations using an O(a) improved (FNAL) sp
ace-time asymmetric fermion action on a 12(3) x 24 quenched lattice at beta
= 5.7 and with c(SW) = 1.57. The mass dependent asymmetry parameter zeta i
s determined non-perturbatively from the energy-momentum dispersion relatio
n. Calculations have been made in the charm and bottom quark mass sectors i
n order to test the zeta dependence of the spectrum, since it is at these h
eavier masses that the asymmetry is expected to be most relevant.