We first discuss that a full supersymmetry algebra cannot be realized
on lattice. This comes from the fact that the Leibniz rule of space-time
derivatives in the continuum cannot hold for finite difference operators
on lattice by the no-go theorem. We then propose a modified Leibniz rule,
called a cyclic Leibniz rule (CLR), on lattice, and consider a complex
supersymmetric quantum mechanics equipped with the CLR.
It is shown that the CLR allows two of four supercharges of the
continuum theory to preserve, while a naive lattice model can realize
one supercharge at the most. A striking feature of our lattice model
is that there are no quantum corrections to potential terms in any
order of perturbation theory. This is one of characteristic properties
of supersymmetric theory in the continuum. It turns out that the
CLR allows to have a non-trivial cohomology and plays a crucial role
in the proof of the non-renormalization theorem.