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In this paper, we demonstrate a high power and high-order random Raman fiber laser based on a 1 km novel tapered fiber (TF). The core diameter of the TF gradually increases from 8 μm to 20 μm. The highest output power amounts to 16.4, 35.4, and 40.1 W for the first (1120 nm), second (1173 nm), and third (1237 nm) order Stokes waves, respectively. The spectrum gets broader with increasing pump power. The full width at half maximum (FWHM) of the first, second, and third-order Stokes waves amounts to 1.2, 1.5, and 3.7 nm. In contrast to the first two order Stokes waves in a half-open cavity, the third-order Stokes wave is generated in a completely open cavity. To the best of our knowledge, this is the highest output power for third-order random Stokes wave.