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In this letter, we propose a new pulse position modulation (PPM) scheme, called expurgated PPM (EPPM), for application in peak power limited communication systems, such as impulse radio (IR) ultra wide band (UWB) systems and free space optical (FSO) communications. Using the proposed scheme, the constellation size and the bit-rate can be increased significantly in these systems. The symbols are obtained using symmetric balanced incomplete block designs (BIBD), forming a set of pair-wise equidistant symbols. The performance of Q-ary EPPM is better than any Q-ary pulse position-based modulation scheme with the same symbol length. Since the code is cyclic, the receiver for EPPM is simpler compared to multipulse PPM (MPPM).