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Pyroelectric infrared (PIR) sensors are widely used as a simple but powerful people presence triggers, e.g., automatic lighting systems. In particular, by alternating the effective polarization of the sensing elements in a PIR sensor, it is possible to determine the relative direction of the movement of an object moving on the motion plane of the PIR sensor. In this paper, we present a novel method of detecting a relative direction of human movement (in eight directions uniformly distributed) with two pairs of PIR sensors whose sensing elements are orthogonally aligned. We have developed a data collection unit with four dual sensing element PIR sensors with modified lenses, and collected data set from six subjects walking in eight directions each. Based on the collected PIR signals, we have performed classification analysis with well known machine learning algorithms, including instance-based learning and support vector machine. Our findings show that with the raw data set captured from two orthogonally aligned PIR sensors with modified lenses, we were able to achieve more than 98% correct detection of direction of movement. We also found that with the reduced feature set composed of three peak values for each PIR sensor, we could achieve 89%-95% recognition accuracy according to machine learning algorithms.