In block transmission systems, blind channel shortening methods are known to be effective to reduce the influence of interblock interference which degrades the performance when the length of a channel impulse response is extremely long. Conventional methods assume that the transmitted signal is uncorrelated; however, this assumption is invalid in practical systems such as OFDM with null carriers and MC-CDMA. In this paper, we consider blind channel shortening methods for block transmissions when the transmitted samples within a block are correlated. First, the channel shortening ability of a conventional method is clarified. Next, a new method which exploits the fact that the transmitted samples in different blocks are uncorrelated is introduced. It is shown that the proposed method can shorten the channel properly under certain conditions. Finally, simulation results of OFDM and MC-CDMA systems are shown to verify the effectiveness of the proposed method compared with a conventional one.