  The truncated Milstein method, which was initially proposed in (Guo, Liu, Mao
and Yue 2018), is extended to the non-autonomous stochastic differential
equations with the super-linear state variable and the H\"older continuous time
variable. The convergence rate is proved. Compared with the initial work, the
requirements on the step-size is also significantly released. In addition, the
technique of the randomized step-size is employed to raise the convergence rate
of the truncated Milstein method.
