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Shannon showed that for the binary multiplying channel (BMC) his inner and outer hounds to the capacity region differ. Schalkwijk gave a simple coding strategy that yields rate pairs outside the Shannon inner bound region. For the case of equal rates in both directions this strategy achieves beyond Shannon's inner bound rate . In this correspondence it is shown that using a result by Slepian and Wolf one can bootstrap the Schalkwijk strategy to find an even larger achievable rate region. In fact, symmetric operation of the BMC now yields a common rate .