We generalize the known method for explicit construction of mirror pairs of
$(2,2)$-superconformal field theories, using the formalism of Landau-Ginzburg
orbifolds. Geometrically, these theories are realized as Calabi-Yau
hypersurfaces in weighted projective spaces. This generalization makes it
possible to construct the mirror partners of many manifolds for which the
mirror was not previously known.