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The tetragonal CF potential splits the Yb$^{3+}$ $^2F_{7/2}$ ground multiplet into two $\\Gamma_6$ and two $\\Gamma_7$ Kramers doublets. We establish the following CF level scheme of the ground multiplet: a $\\Gamma_6$ ground state, with the two $\\Gamma_7$ states at 2 cm$^{-1}$, 95 cm$^{-1}$ and the other $\\Gamma_6$ state at 239 cm$^{-1}$. 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