  Dissipative dynamics of quantum systems can be classified topologically based
on the correspondence between the Lindbladian in the
Gorini-Kossakowski-Sudarshan-Lindblad equation and the non-Hermitian
Hamiltonian in the Schr\"{o}dinger equation. While general non-Hermitian
Hamiltonians are classified into 38 symmetry classes, previous studies have
shown that the Lindbladians are classified into 10 symmetry classes due to a
physical constraint. In this work, however, we unveil a topological
classification of Lindbladians based on shifted sublattice symmetry (SLS),
which can increase the number of symmetry classes for the Lindbladians. We
introduce shifted SLS so that the Lindbladian can retain this symmetry and take
on the same role as SLS for the topological classification. For verification,
we construct a model of a dissipative quantum system retaining shifted SLS and
confirm the presence of edge states protected by shifted SLS. Moreover, the
relationship between the presence of shifted SLS protected edge states and the
dynamics of an observable quantity is also discussed.
