  We propose a novel tensor network representation for two-dimensional
Yang-Mills theories with arbitrary compact gauge groups. In this method, tensor
indices are directly given by group elements with no direct use of the
character expansion. We apply the tensor renormalization group method to this
tensor network for $SU(2)$ and $SU(3)$, and find that the free energy density
and the energy density are accurately evaluated. We also show that the singular
value decomposition of a tensor has a group theoretic structure and can be
associated with the character expansion.
