  General Relativity and its higher derivative extensions have symmetric
teleparallel reformulations in terms of the non-metricity tensor within a
torsion-free and flat geometry. These notes present a derivation of the exact
propagator for the most general infinite-derivative, even-parity and generally
covariant theory in the symmetric teleparallel spacetime. The action made up of
the non-metricity tensor and its contractions is decomposed into terms
involving the metric and a gauge vector field and is found to complement the
previously known non-local ghost- and singularity-free theories.
