  The rare phenomenon of ribbon-like hard X-ray (HXR) sources up to 100 keV
found in the 2005 May 13 M8.0 flare observed with the \textit{Reuven Ramaty
High Energy Solar Spectroscopic Imager} provides detailed information on the
spatial distribution of flare HXR emission. In this Letter, we further
investigate the characteristics of HXR emission in this event using imaging
spectroscopy, from which we obtain spatially resolved HXR spectral maps during
the flare impulsive phase. As a result we found, along a flare ribbon, an
anticorrelation relationship between the local HXR flux and the local HXR
spectral index. We suggest that this can be regarded as a spatial analog of the
well-known temporal soft-hard-soft spectral evolution pattern of the integrated
HXR flux. We also found an anticorrelation between HXR spectral index and local
electric field along the ribbon, which suggests the electron acceleration by
the electric field during flares.
