The authors introduce a quantum Fermion stochastic integral for non adapted integrands. Their method makes use of Guichardet's representation of Fock spaces in the form \(L^2 (\Gamma)\), where \(\Gamma\) is taken as the set of all finite subsets of a given non-atomic, separable, \(\sigma\)-finite, measurable space. The authors first establish an isomorphism between \(L^2 (\Gamma)\) and \(L^2 (C(H))\), where \(C(H)\) denotes the Clifford algebra over a given Hilbert space \(H\). A gradient and its adjoint are then defined in \(L^2 (C(H))\) which allow to derive the notion of a quantum Fermion stochastic integral.