  We propose a second renormalization group (SRG) in the triad representation
of tensor networks. The SRG method improves two parts of the triad tensor
renormalization group, which are the decomposition of intermediate tensors and
the preparation of isometries, taking the influence of environment tensors into
account. Every fundamental tensor including environment tensor is given as a
rank-3 tensor, and the computational cost of the proposed algorithm scales with
${\cal O}(\chi^5)$ employing the randomized SVD where $\chi$ is the bond
dimension of tensors. We test this method in the classical Ising model on the
two dimensional square lattice, and find that numerical results are obtained in
good accuracy for a fixed computational time.
