This paper proposes a novel digital predistorter (DPD) for 2⨯2 nonlinear multiple-input-multiple-output (MIMO) transmitters. It is intended to compensate for the nonlinear distortion and the memory effects generated by power amplifiers (PAs) in addition to the crosstalk effects. The novel polynomial DPD performs comparably to the state-of-art Generalized Memory Polynomial for Nonlinear Crosstalk model (GMPNLC), while requiring much less coefficients. However, it exhibits much higher performances compared to Generalized Memory Polynomial for Linear Crosstalk (GMPLC) DPD for the same problem size.