  A new approach for tree-level amplitudes with multiple fermion lines is
presented. It mainly focuses on the simplification of fermion lines. By
calculating two vectors recursively without any matrix multiplications, the
result of a fermion line is reduced to a very compact form depending only on
the two vectors. The comparisons with other packages are presented, and the
results show that our package FDC gives a very good performance in the
processes of multiple fermion lines with this new approach and some other
improvements. A further comparison with WHIZARD shows that this new approach
has a competitive efficiency in computing pure amplitude square without phase
space integration.
