The production of ultracold molecules with their rich internal structure is currently attracting considerable interest 1-4 . For future experiments, it will be important to efficiently transfer these molecules from their initial internal quantum state at production to other quantum states of interest. Transfer tools such as optical Raman schemes 5,6 , radiofrequency transitions (see, for example, ref. 7) or magnetic field ramping 8,9 exist, but are either technically involved or limited in their applicability. Here, we demonstrate a simple, highly efficient hybrid transfer method that overcomes a number of the previous limitations. The scheme is based on magnetically tuned mixing of two neighbouring molecular levels, which enables otherwise forbidden radiofrequency transitions between them. By repeating this process at various magnetic fields, molecules can be successively transported through a large manifold of quantum states. Applying nine transfers, we convert very weakly bound Feshbach molecules to a much more deeply bound level with a binding energy corresponding to 3.6 GHz. As an important spin-off of our experiments, we demonstrate a high-precision spectroscopy method for investigating level crossings.Radiofrequency has important applications for ultracold molecules, such as spectroscopy 7,10-14 and molecule production [15][16][17] . Using radiofrequency to transfer ground-state molecules between states of different vibrational quantum numbers, as demonstrated here, is not obvious. For simple molecular potentials, transition matrix elements for magnetic dipole transitions between different vibrational levels are expected to vanish on the basis of an overlap argument of the spatial wavefunctions. However, for real molecules such as Rb 2 , the situation is more complex, for example, owing to exchange interaction, hyperfine structure and the Zeeman effect. The combined effect of these interactions induces mixing of states with different vibrational quantum numbers, leading to new eigenstates between which radiofrequency transitions can be driven (see the Methods section). This mixing effect is maximal at avoided crossings. (As a consequence, it is important for radiofrequency spectroscopy at Feshbach resonances 12 .)We carry out our experiments with a