We report the first observation of two wobbling bands in $^{183}$Au, both of which were interpreted as the transverse wobbling (TW) band but with different behavior of their wobbling energies as a function of spin. It increases (decreases) with spin for the positive (negative) parity configuration. The crucial evidence for the wobbling nature of the bands, dominance of the $E2$ component in the $Delta I = 1$ transitions between the partner bands, is provided by the simultaneous measurements of directional correlation from the oriented states (DCO) ratio and the linear polarization of the $gamma$ rays. Particle rotor model calculations with triaxial deformation reproduce the experimental data well. A value of spin, $I_m$, has been determined for the observed TW bands below which the wobbling energy increases and above which it decreases with spin. The nucleus $^{183}$Au is, so far, the only nucleus in which both the increasing and the decreasing parts are observed and thus gives the experimental evidence of the complete transverse wobbling phenomenon.
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