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To overcome the problem that the transmission rate of a multicast channel is limited by the user with the worst channel quality, which causes the total system throughput to be low, the use of both multicast and unicast channels for multicast service is considered in this letter. Unicast channels, in addition to a multicast channel, are allocated to users with signal-to-noise ratios (SNRs) lower than a predefined threshold in order to enable the increase of the transmission rate of the multicast channel. The used unicast channels consume additional radio resource. It is examined whether use of such unicast channels can raise the spectral efficiency defined as the total system throughput normalized by the total consumed bandwidth. The optimal value of the threshold SNR is derived by maximizing the spectral efficiency. When a unicast channel is additionally allocated for multicast service, two decoding schemes are considered: one is to use only the signal of a unicast channel, and the other is to use and combine both the signals of multicast and unicast channels. Numerical examples are presented to show the performance gains obtained by using unicast channels in addition to a multicast channel.