  In this paper we study subdiffusion in a system with a thin membrane. At the
beginning, the random walk of a particle is considered in a system with a
discrete time and space variable and then the probability describing the
evolution of the particle's position (Green's function) is transformed into a
continuous system. Two models are considered differing here from each other
regarding the assumptions about how the particle is stopped or reflected by the
membrane when the particle attempts to pass through the membrane fails. We show
that for a system in which a membrane is partially permeable with respect to
both its sides the Green's functions obtained for both models within the {\it
continuous time random walk formalism} are equivalent to each other and
expressed by the functions presented in the paper: T. Koszto{\l}owicz, Phys.
Rev. E \textbf{91}, 022102 (2015), except the values defined at the membrane's
surfaces. We also show that for a system with a one--sidedly fully permeable
membrane, the Green's functions obtained within both models are not equivalent
to each other.
  We also present the generalized method of images which provides the Green's
functions for the membrane system, obtained in this paper. This method, which
has a simple physical interpretation, is of a general nature and, in our
opinion, can be used to find the Green's functions for a system with a thin
membrane in which various models of subdiffusion can be applied. As an example,
we find the Green's functions for the particular case of a `slow--subdiffusion'
process in a system with a thin membrane.
