An all-optical generation of a microwave carrier at $21\mathrm{GHz}$ that incorporates a double-Brillouin frequency shifter is presented. The frequency shift of $\sim 21\mathrm{GHz}$ 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 $21.3968\mathrm{GHz}$ , and the carrier phase noise as low as $-58.67\mathrm{dBc}∕\mathrm{Hz}$ is achieved.