In [1] and [2], authors proposed two efficient crossover predistortion schemes which are capable to compensate simultaneously HPA nonlinearity and crosstalk effects in MIMO systems. The crosstalk model considered in these papers was memoryless one. However, memory effects of crosstalk can no longer be ignored due to the broadband transmitted signal. Then, in this paper, we demonstrate the effect of memory crosstalk on the Crossover Neural Network Predistorter (CO-NNPD) proposed in [1]. Along, we propose a new crossover predistortion structure based on this conventional CO-NNPD which is capable to enhance good performance in MIMO OFDM systems in presence of HPA nonlinearities with taken into account the memory effects of crosstalk. The Levenberg-Marquardt algorithm (LM) is used for neural network training, which has proven [3] to exhibit a very good performance with lower computation complexity and faster convergence than other algorithms used in literature. This paper is supported with simulation results for the Alamouti STBC MIMO OFDM system in terms of Bit Error Rate (BER) in Rayleigh fading channel.