  This paper is dedicated to the global well-posedness issue of the
compressible Oldroyd-B model in the whole space $\R^d$ with $d\ge2$. It is
shown that this set of equations admits a unique global solution in a certain
critical Besov space provided the initial data, but not necessarily the
coupling parameter, is small enough. This result extends the work by Fang and
the author [{J. Differential Equations}, {256}(2014), 2559--2602] to the
non-small coupling parameter case.
