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In this letter, we present a novel, with-memory precoding scheme for N-continuous OFDM, which is based on the decomposition of a relevant matrix into its null space and orthogonal complement subspace. The transmitted data can be fully recovered by the proposed scheme, while the out-of-band emission performance is retained as other N-continuous OFDM signals. The data rate loss is reduced to half compared to the memory-less scheme. Bit-error-rate performance can be improved by exploiting the redundant information in the subsequent OFDM symbol.