Polar molecules have bright prospects for novel quantum gases with long-range and anisotropic interactions(1), and could find uses in quantum information science(2) and in precision measurements(3-5). However, high-density clouds of ultracold polar molecules have so far not been produced. Here, we report a key step towards this goal. We start from an ultracold dense gas of loosely bound (KRb)-K-40-Rb-87 Feshbach molecules(6,7) with typical binding energies of a few hundred kilohertz, and coherently transfer these molecules in a single transfer step into a vibrational level of the ground-state molecular potential bound by more than 10 GHz. Starting with a single initial state prepared with Feshbach association(8), we achieve a transfer effIciency of 84%. Given favourable Franck-Condon factors(9,10), the presented technique can be extended to access much more deeply bound vibrational levels and those exhibiting a significant dipole moment.