To suppress intercell interference for three-cell half-duplex relay systems, joint interference suppression and multiuser detection (MUD) schemes that estimate weight coefficients by the recursive least-squares (RLS) algorithm have been proposed but show much worse bit error rate (BER) performance than maximum likelihood detection (MLD). To improve the BER performance, this paper proposes a joint interference suppression and MUD scheme that estimates the weight coefficients by eigenvalue decomposition. The proposed scheme carries the same advantages as the conventional RLS based schemes; it does not need channel state information (CSI) feedback while incurring much less amount of computational complexity than MLD. In addition, it needs to know only two out of three preambles used in the system. Computer simulations of orthogonal frequency-division multiplexing (OFDM) transmission under three-cell and frequency selective fading conditions are conducted. It is shown that the eigendecomposition-based scheme overwhelmingly outperforms the conventional RLS-based scheme although requiring higher computational complexity.