This study proposes a novel signal processing method for detecting the vital signs of multiple adjacent subjects using a 24 GHz frequency modulated continuous wave Doppler radar. Radar-based vital signs sensors have attracted significant attention because of their contactless and unobtrusive mode of measurement. However, limited-bandwidth, fixed-beam systems have been restricted to single subjects because a high resolution is required to detect the vital signs of multiple adjacent subjects. As the range resolution is determined by the frequency bandwidth, a novel method is proposed that doubles the effective frequency bandwidth by using a modified waveform. The proposed method can distinguish between two subjects sitting 40 cm apart, overcoming the 60 cm Rayleigh resolution for a frequency bandwidth of 250 MHz. The computational complexity of the proposed method is considerably low when compared with high-resolution algorithms such as the multiple signal classification algorithm. Furthermore, the method easily suppresses stationary clutter by using phase deviation. To validate the performance of the proposed method, experiments were conducted with two subjects lying side by side on a bed. The results indicate the excellent performance, with enhanced range and high detection accuracy. This method has many potential applications, including monitoring infants and sleep apnea patients.