  We present results of an exact diagonalization calculation of the spectral
function $A(\bf k, \omega)$ for a single hole described by the $t$--$J$ model
propagating on a 32--site square cluster. The minimum energy state is found at
a crystal momentum ${\bf k} = ({\pi\over 2}, {\pi\over 2})$, consistent with
theory, and our measured dispersion relation agrees well with that determined
using the self--consistent Born approximation. In contrast to smaller cluster
studies, our spectra show no evidence of string resonances. We also make a
qualitative comparison of the variation of the spectral weight in various
regions of the first Brillouin zone with recent ARPES data.
