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We report on the development of a photoacoustic sensor for the detection of formaldehyde (CH2O) using a thermoelectrically cooled distributed-feedback quantum cascade laser operating in pulsed mode at 5.6 mm. A resonant photoacoustic cell, equipped with four electret microphones, is excited in its first longitudinal mode at 1,380 Hz. The absorption line at 1,778.9 cm-1 is selected for CH2O detection. A detection limit of 150 parts per billion in volume in nitrogen is achieved using a 10 seconds time constant and 4 mW laser power. Measurements in ambient air will require water vapour filters.