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In this paper, the novel subcarrier assignment for achieving large channel capacity as well as small PAPR of transmitted signal is proposed in downlink multiuser OFDM system. In the proposed assignment, some resource blocks are acceptably assigned to the second-best mobile user. As a result, there are some candidates for assigning the resource block to mobile user. In the proposed technique, we choose the assignment pattern among the candidates as the peak to average power (PAPR) of transmitted signal becomes small. Even if the total channel capacity becomes smaller, PAPR becomes small. From the computer simulation, as the number of resource blocks assigned to the second best mobile station becomes larger, the PAPR reduction is more effective but the channel capacity decreases. Therefore, the proposed assignment establishes the PAPR - Channel Capacity trade off. However, as the number of mobile users increases, the base station has the more opportunities to find the mobile station having larger SNR. It is user diversity effect. Owing to user diversity, we also confirm that the PAPR - channel capacity trade off becomes better when the number of mobile users becomes larger.