Using a deep autoencoder (DAE) for end-to-end communication in multiple-input multiple-output (MIMO) systems is a novel concept with significant potential. DAE-aided MIMO has been shown to outperform singular-value decomposition (SVD)-based precoded MIMO in terms of bit error rate (BER). This paper proposes embedding left- and right-singular vectors of the channel matrix into DAE encoder and decoder to further improve the performance of the MIMO DAE. SVDembedded DAE largely outperforms theoretic linear precoding in terms of BER. This is remarkable since it demonstrates that DAEs have significant potential to exceed the limits of current system design by treating the communication system as a single, end-to-end optimization block. Based on the simulation results, at SNR=10dB, the proposed SVD-embedded design can achieve a BER of about $10^{-5}$ and reduce the BER at least 10 times compared with existing DAE without SVD, and up to 18 times compared with theoretical linear precoding. We attribute this to the fact that the proposed DAE can match the input and output as an adaptive modulation structure with finite alphabet input. We also observe that adding residual connections to the DAE further improves the performance.