We present an efficient new method termed LN for propagating biomolecular dynamics according to the Langevin equation that arose fortuitously upon analysis of the range of harmonic validity of our normal-mode scheme LIN. LN combines force linearization with force splitting techniques and disposes of LIN'S computationally intensive minimization (anharmonic correction) component. Unlike the competitive multiple-timestepping (MTS) schemes today-formulated to be symplectic and time-reversible-LN merges the slow and fast forces via extrapolation rather than "impulses;" the Langevin heat bath prevents systematic energy drifts. This combination succeeds in achieving more significant speedups than these MTS methods which are Limited by resonance artifacts to an outer timestep less than some integer multiple of half the period of the fastest motion (around 4-5 fs for biomolecules). We show that LN achieves very good agreement with small-timestep solutions of the Langevin equation in terms of thermodynamics (energy means and variances), geometry, and dynamics (spectral densities) for two proteins in vacuum and a large water system. Significantly, the frequency of updating the slow forces extends to 48 fs or more, resulting in speedup factors exceeding 10. The implementation of LN in any program that employs force-splitting computations is straightforward, with only partial second-derivative information required, as well as sparse Hessian/vector multiplication routines. The linearization part of LN could even be replaced by direct evaluation of the fast components. The application of LN to biomolecular dynamics is well suited for configurational sampling, thermodynamic, and structural questions.