  We derive new four-dimensional partial differential equation with the
isospectral Lax representation by shrinking the symmetry algebra of the reduced
quasi-classical self-dual Yang--Mills equation. Then we find a recursion
operator for the obtained equation and construct B{\"a}cklund transformations
between this equation and the reduced quasi-classical self-dual Yang--Mills
equation as well as the four-dimensional Mart{\'{\i}}nez Alonso--Shabat
equation
