An all-optical generation of a microwave carrier at 21 GHz that incorporates a double-Brillouin frequency shifter is presented. The frequency shift of approximately 21 GHz is achieved by generating the second-order Brillouin Stokes signal from the Brillouin pump. This is accomplished through the circulation and isolation of its first-order Stokes signal in the optical fiber. The Brillouin pump signal is heterodyned with its second-order Brillouin Stokes signal at a high-speed photodetector, and the output beating frequency is equal to the offset between these two signals. The generated microwave carrier is measured at 21.3968 GHz, and the carrier phase noise as low as -58.67 dBc/Hz is achieved.