An AlGaAs laser diode (slave laser) has been frequency-locked to a Fabry-Perot interferometer which is locked to a diode laser (master laser) beam frequency-locked to the D(2) line of a Cs atomic beam. Frequency-locking of the Fabry-Perot interferometer to the master laser beam frequency-locked to a resonance line of an atomic beam greatly improves its long-term frequency stability. Therefore, it substantially improves the slave laser diode frequency stability frequency-locked to it. The measured frequency stabilities show that the very high frequency stability of the D(2) line of a Cs atomic beam has been transferred to the slave laser by this frequency-locking system within 1.6 x 10(-11)(10s). This system can be used for building a network of diode lasers with high frequency stability.