  We explain a new construction of self-dual string solutions to the
non-abelian two-form self-duality equation proposed in \cite{CK}. This class of
self-dual strings is determined by the BPS monopoles in four-dimensions and the
self dual string charge is given by the charge of the monopole. Our
construction covers the SO(4) invariant self-dual string solutions found
previously. We have also constructed, based on the 't Hooft-Polyakov monopole,
a singular solution that describes two finitely separated M5-branes meeting
midway in between. We comment that as BPS monopoles are generally given by the
Nahm construction, our construction suggests that a generalized Nahm transform
may exist for the non-abelian self-dual strings.
