We present a precoded reduced-complexity soft detection (PRCSD) algorithm for multiple-input multiple-output (MIMO) systems. The linear operations at both transmit and receive sides based on complex Householder transform convert the MIMO channel to be multiple-diagonal, spatially partial-response-like, so that error propagation is alleviated when applying reduced-complexity soft detection at the receiver. The transform results in unitary precoding and feedforward matrices so that neither transmit power boost nor noise enhancement is present. Performance analysis based on pairwise error probability (PEP) shows that PRCSD achieves larger diversity advantage than existing precoding and multiple-beamforming (MB) schemes, which basically attempt to transmit signals through diagonal independent sub-channels and thus may suffer a diversity loss. PRCSD can achieve full diversity as maximum likelihood (ML) detection in some scenarios while reducing complexity significantly.