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In this study, the authors propose a novel blind adaptive minor subspace tracking interference alignment (BAMST-IA) scheme for slowly fading two-way interference channel. In this scheme, a new frame structure is designed to exploit the dependency of the channels between consecutive fading blocks. Then, the IA problem is reformulated as a minor subspace tracking problem, and the low computational complexity fast data projection method algorithm is integrated with the BAMST-IA scheme to update the IA solutions. Moreover, the update uses only observed data without any channel state information, thus requires lower signalling overhead. Simulation results are presented to show that the proposed BAMST-IA scheme is fit for slowly fading channels.