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We consider a two-user multiple-input multiple-output (MIMO) interference channel (IC), where a single data stream is transmitted and each receiver applies the minimum mean square error (MMSE) filter. In this paper, we study an open problem on the computation of the Pareto boundary of the achievable rate region by optimal joint transmit/receive beamforming design. The Pareto boundary can be divided by two turning points into the weak Pareto boundary and the strict Pareto boundary. The weak Pareto boundary and turning points can be computed exactly. For the strict Pareto boundary, we propose a computationally efficient method called iterative alternating algorithm (IAA) to maximize the rate of one user while the rate of the other user is fixed. Numerical simulations show that the IAA provides a better lower bound on the strict Pareto boundary compared with the existing methods.