We developed a noncontact measurement system for monitoring the respiration of multiple people using millimeter-wave array radar. To separate the radar echoes of multiple people, conventional techniques cluster the radar echoes in the time, frequency, or spatial domain. Focusing on the measurement of the respiratory signals of multiple people, we propose a method called respiratory-space clustering, in which individual differences in the respiratory rate are effectively exploited to accurately resolve the echoes from human bodies. The proposed respiratory-space clustering can separate echoes, even when people are located close to each other. In addition, the proposed method can be applied when the number of targets is unknown and can accurately estimate the number and positions of people. We perform multiple experiments involving five or seven participants to verify the performance of the proposed method, and quantitatively evaluate the estimation accuracy for the number of people and the respiratory intervals. The experimental results show that the average root-mean-square error in estimating the respiratory interval is 196 ms using the proposed method. The use of the proposed method, rather the conventional method, improves the accuracy of the estimation of the number of people by 85.0%, which indicates the effectiveness of the proposed method for the measurement of the respiration of multiple people.