The frequency stability of a 1560-nm diode laser, whose second harmonic was locked to (87)Rb sub-Doppler lines, was characterized by measuring the beat frequency relative to a 780-nm reference laser that was locked to sub-Doppler lines of another rubidium cell. The square root of the Allan variance reached a minimum value of 7.5 x 10(-12) in 1 s, which corresponded to frequency variations of 1.44 kHz for the 1560-nm laser. The frequency reproducibility of the system was approximately 1 x 10(-9). These values are better than those that can be achieved by locking to Doppler-broadened transitions at the 1550-nm wavelength band.