  We present an improved variant of the in-medium similarity renormalization
group (IM-SRG) based on the Magnus expansion. In the new formulation, one
solves flow equations for the anti-hermitian operator that, upon
exponentiation, yields the unitary transformation of the IM-SRG. The resulting
flow equations can be solved using a first-order Euler method without any loss
of accuracy, resulting in substantial memory savings and modest computational
speedups. Since one obtains the unitary transformation directly, the
transformation of additional operators beyond the Hamiltonian can be
accomplished with little additional cost, in sharp contrast to the standard
formulation of the IM-SRG. Ground state calculations of the homogeneous
electron gas (HEG) and $^{16}$O nucleus are used as test beds to illustrate the
efficacy of the Magnus expansion.
