  In a recent paper [TMP, 200:1 (2019), 966--984] by the authors, a series of
integrable discrete autonomous equations on a square lattice with a
non-standard structure of generalized symmetries is constructed. We build
modified series by using discrete non-point transformations. We use both
non-invertible linearizable transformations and non-point transformations
invertible on solutions of the discrete equation. As a result, we get several
series of new examples of discrete equations along with their generalized
symmetries and master symmetries. The generalized symmetries constructed give
new integrable examples of five- and seven-point differential-difference
equations together with their master symmetries. In the case of discrete
equations, the method of constructing non-invertible linearizable
transformations by using conservation laws is considered, apparently, for the
first time.
