This letter provides a tight upper bound on the bit error rate (BER) over the Nakagami-m fading channel for the dual carrier modulation (DCM) scheme, which is adopted by the multi-band orthogonal frequency division multiplexing (MB-OFDM) ultra-wideband (UWB) system. Its tightness is verified with the existing result for Rayleigh fading channel, i.e., for m=1, which would be also valid for a more general fading environment.