  We derive general form of finite-dimensional approximations of path integrals
for both bosonic and fermionic canonical systems in terms of symbols of
operators determined by operator ordering. We argue that for a system with a
given quantum Hamiltonian such approximations are independent of the type of
symbols up to terms of $O(\epsilon)$, where $\epsilon$ is infinitesimal time
interval determining the accuracy of the approximations. A new class of such
approximations is found for both c-number and Grassmannian dynamical variables.
The actions determined by the approximations are non-local and have no
classical continuum limit except the cases of $pq$- and $qp$-ordeeing. As an
explicit example the fermionic oscillator is considered in detail.
