Clusters of galaxies are among the best candidates for particle acceleration sources in the universe, a signature of which is non-thermal hard X-ray emission from the accelerated relativistic particles. We present early results on Suzaku observations of non-thermal emission from Abell 3376, which is a nearby on-going merger cluster. Suzaku observed the cluster twice, while focusing on the cluster center containing the diffuse radio emission to the east, and a cluster peripheral region to the west. For both observations, we detected no excess hard X-ray emission above the thermal cluster emission. An upper limit on the non-thermal X-ray flux of 2.1 |$\times$| 10|$^{-11}$| erg cm|$^{-2}$|s|$^{-1}$| (15–50 keV) at the 3|$\sigma$| level from a 34|$^\prime$||$\times$| 34|$^\prime$| region, derived with the Hard X-ray Detector (HXD), is similar to that obtained with the BeppoSAX/PDS. Using the X-ray Imaging Spectrometer (XIS) data, the upper limit on the non-thermal emission from the West Relic is independently constrained to be |$<$|1.1 |$\times$| 10|$^{-12}$| erg s|$^{-1}$| cm|$^{-2}$| (4–8 keV) at the 3|$\sigma$| level from a 122 arcmin|$^2$| region. Assuming Compton scattering between relativistic particles and the cosmic microwave background photons, the intracluster magnetic field |$B$| is limited to be |$>$|0.03|$\mu$|G (HXD) and |$>$|0.10|$\mu$|G (XIS).

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