  We present and implement an efficient variational method to simulate
two-dimensional finite size fermionic quantum systems by fermionic projected
entangled pair states. The approach differs from the original one due to the
fact that there is no need for an extra string-bond for contracting the tensor
network. The method is tested on a bi-linear fermionic model on a square
lattice for sizes up to ten by ten where good relative accuracy is achieved.
Qualitatively good results are also obtained for an interacting fermionic
system.
