  We apply the technique of complex paths to obtain Hawking radiation in
different coordinate representations of the Schwarzschild space-time. The
coordinate representations we consider do not possess a singularity at the
horizon unlike the standard Schwarzschild coordinate. However, the event
horizon manifests itself as a singularity in the expression for the
semi-classical action. This singularity is regularized by using the method of
complex paths and we find that Hawking radiation is recovered in these
coordinates indicating the covariance of Hawking radiation. This also shows
that there is no correspondence between the particles detected by the model
detector and the particle spectrum obtained by the quantum field theoretic
analysis -- a result known in other contexts as well.
