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This paper presents a MIMO two-way relaying scheme where the transceiver filter at the Relay Station (RS) processes the data using a variant of the Affine Projection Algorithm (APA), known as Partial Rank Algorithm (PRA). The relaying technique used is Amplify and Forward scheme (AF). The modulation technique used at the nodes S1 and S2 is Quadrature Phase Shift Keying (QPSK). The performance of PRA algorithm is verified by comparing its Mean-Square error performance (MSE) and Bit Error Rate (BER) with that of a transceiver filter based on Normalized Least Mean Square (NLMS) algorithm. The computational complexity of the algorithm is also tabulated.