We describe a wavelet transform analysis of the ROSAT Position Sensitive Proportional Counter images of the Coma Cluster. On small scales, less than or equal to 1', the wavelet analysis shows substructure dominated by two extended sources surrounding the two brightest cluster galaxies, NGC 4874 and NGC 4889. On slightly larger scales, similar to 2', the wavelet analysis reveals a filament of X-ray emission originating near the cluster's center, curving to the south and east for similar to 25' in the direction of the galaxy NGC 4911, and ending near the galaxy NGC 4921. These results extend earlier ROSAT observations and further indicate the complex nature of the cluster's core. We consider two possible explanations for the production of the filamentary feature from interactions of the main cluster with a merging group. The feature could arise from either ram pressure stripped gas or a dark matter perturbation of tidally stripped material.