Filter Bank Multi-Carrier (FBMC) system based on offset Quadrature Amplitude Modulation (offset-QAM) combined with Multiple-Input-Multiple-Output (MIMO) technique faces great challenges. The inherent imaginary interference of FBMC seriously impacts the performance of the Maximum Likelihood (ML) detection technique in MIMO transmission. The application of the Alamouti code is also hindered. In this paper, we present a data-compressed transmission method based on non-sinusoidal orthogonal transformation, which can recover the bi-orthogonality of FBMC and eliminate the imaginary interference. Thereby, the combination of FBMC and MIMO as well as the application of ML technique and Alamouti code are realized. Specifically, we first consider the Walsh transform, which belongs to the non-sinusoidal orthogonal transform, and utilize its property that can reduce the transmission bandwidth to recover the orthogonality of the FBMC in the frequency domain. Secondly, we construct the discrete transmission model of the system and generate the orthogonal compression matrix utilizing the fast Walsh transform. Then, we analyze the multi-frame transmission, calculate the frames interference, and improve the signal-to-interference ratio again by adding guard time slots. Finally, we construct the MIMO transmission model and complete the theoretical analysis. Simulation results show that the proposed scheme has a robust MIMO transmission performance. ML and Alamouti code techniques perform the same as Orthogonal Frequency Division Multiplex in bi-orthogonal FBMC.