Tensor renormalization group (TRG) has attractive features like the absence of sign problems
and the accessibility to the thermodynamic limit, and many applications to lattice field theories
have been reported so far. However it is known that the TRG has a fictitious fixed point that
is called the CDL tensor and that causes less accurate numerical results. There are improved
coarse-graining methods that attempt to remove the CDL structure from tensor networks. Such
approaches have been shown to be beneficial on two dimensional spin systems. We discuss how
to adapt the removal of the CDL structure to tensor networks including fermions, and numerical
results that contain some comparisons to the plain TRG, where significant differences are found,
will be shown. The detailed discussion of this work is given in ref. [1].