Parasitic antenna elements with tunable terminations can be used for interference suppression in multi-antenna systems without using the degrees of freedom. The authors have proposed a fast non-iterative algorithm for optimizing the termination conditions. However, this method cannot be used for suppressing the interference from unknown systems since it requires the channel state information. In this paper, a fast non-iterative algorithm based on the correlation matrix, which can be obtained even from unknown interference sources, is proposed for the multi-antenna system with parasitic antenna elements. The correlation matrix including both receiving and parasitic antennas can be estimated from a few observations of the signals even without receiving signals at the parasitic antenna. By using this correlation matrix, the power of the interference with the arbitrary termination conditions can be easily estimated. Therefore, the termination condition, which minimizes the interference power, can be calculated without knowledge of the channel state information or additional estimations. The results of a numerical analysis indicate that proposed method works well in suppressing the interference without the perfect channel state information.