  We solve the gaugino Dirac equation on a smeared intersecting five-brane
solution in E_8\times E_8 heterotic string theory to search for localized
chiral zeromodes on the intersection. The background is chosen to depend on the
full two-dimensional overall transverse coordinates to the branes. Under some
appropriate boundary conditions, we compute the complete spectrum of zeromodes
to find that, among infinite towers of Fourier modes, there exist only three
localized normalizable zeromodes, one of which has opposite chirality to the
other two. This agrees with the result previously obtained in the domain-wall
type solution, supporting the claim that there exists one net chiral zeromode
localized on the heterotic five-brane system.
