The nature of two high-spin bands in 136Nd built on the two-quasiparticle configuration πh211/2, predicted by the triaxial projected shell model as good candidates of transverse wobbling bands, are investigated experimentally. The mixing ratio of one ΔI=1 transition connecting the one-phonon and the zero-phonon wobbling bands is established from a high-statistics JuroGam II γ-ray spectroscopy experiment by using the combined angular correlation and linear polarization method. The resulting wobbling excitation energy and ratios of reduced electromagnetic transition probabilities are in good agreement with results of a new particle-rotor model which rigidly couples the total angular momentum of two quasiparticles to a triaxial core in an orthogonal geometry, confirming thus the transverse wobbling nature of the bands.