We report results of hard X-Ray observations of the clusters Coma, Abell 496, Abell754, Abell 1060, Abell 1367, Abell2256 and Abell3558 using RXTE data from the NASA HEASARC public archive. Specifically we searched for clusters with hard x-ray emission that can be fitted by a power law because this would indicate that the cluster is a source of non-thermal emission. We are assuming the emission mechanism proposed by Vahk Petrosian where the inter cluster space contains clouds of relativistic electrons that by themselves create a magnetic field and emit radio synchrotron radiation. These relativistic electrons Inverse-Compton scatter Microwave Background photons up to hard x-ray energies. The clusters that were found to be sources of non-thermal hard x-rays are Coma, Abell496, Abell754 and Abell 1060.