This paper proposes a MIMO-OFDM precoder that can minimize a BER upper bound of the maximum likelihood detector (MLD) under a non-cooperative downlink multicell co-channel interference (CCI) environment. Since there is no cooperation among base stations (BSs), it is assumed that information on the interference can be estimated at a mobile station (MS) and then fed back to the desired BS for the precoder. The proposed scheme controls its precoding parameters under a transmit power constraint so as to minimize the BER upper bound, which is derived from the pairwise error probability (PEP) averaged with respect to CCI plus noise. Computer simulations demonstrate that the proposed precoder can effectively improve BER performance of cell edge users and is superior in terms of BER to the eigenmode and the minimum mean squared error (MMSE) precoded transmissions which aim to maximize the channel capacity and to minimize MSE, respectively.