  We present new recursion operators for (shadows of nonlocal) symmetries of
the 4D Mart\'inez Alonso-Shabat equation $u_{ty} = u_z u_{xy} - u_y u_{xz}$,
and we show that their actions can produce new symmetries which are not
contained in the Lie algebra of nonlocal symmetries presented in
[I.S.Krasil'shchik, P.Voj\v{c}\'{a}k, On the algebra of nonlocal symmetries for
the 4D Mart\'inez Alonso-Shabat equation. J. of Geom. and Phys. 163, (2021),
104122, (arXiv:2008.10281v1)]. To this end, we construct a non-Abelian covering
of the equation in question using the Lax pair with two non-removable
parameters.
