Magnetic properties of the insulating state of the organic superconductor, β-[(CH3)4N][Pd(dmit)2]2

β-[(CH3)4N][Pd(dmit)2]2, which shows a superconducting transition at 6.2 K under a pressure of 6.5 kbar, is semiconducting in resistance at ambient pressure. Electronic properties was examined by 1H-NMR measurements at ambient pressure and under pressure. We found a magnetic transition at 12 K. The amplitude of the magnetization is estimated to be 0.22 μB per Pd(dmit)2-dimer. Static magnetic susceptibility measured by SQUID shows a small temperature dependence. The transition temperature was found to decrease slightly under pressure, and suddenly disappeared in the metallic state at 6.5 kbar. We discuss how to understand the electronic state of this system.