  In the recent paper [1] the classification of non-unitary representations of
the three dimensional superconformal group has been constructed. From AdS/CFT
they must correspond to N=1 supermultiplets containing partially massless
fields in $AdS_4$. Moreover, the simplest example of such supermultiplets which
contains a partially massless spin-2 was explicitly constructed. In this paper
we extend this result and develop explicit Lagrangian construction of general
N=1 supermultiplets containing partially massless fields with arbitrary
superspin. We use the frame-like gauge invariant description of partially
massless higher spin bosonic and fermionic fields. For the two types of the
supermultiplets (with integer and half-integer superspins) each one containing
two partially massless bosonic and two partially massless fermionic fields we
derive the supertransformations leaving the sum of four their free Lagrangians
invariant such that the $AdS_4$ superalgebra is closed on-shell.
