  In this paper, we develop a new explicit scheme called modified truncated
Milstein method which is motivated by truncated Milstein method proposed by Guo
(2018) and modified truncated Euler-Maruyama method introduced by Lan (2018).
We obtain the strong convergence of the scheme under local boundedness and
Khasminskii-type conditions, which are relatively weaker than the existing
results, and we prove that the convergence rate could be arbitrarily close to 1
under given conditions. Moreover, exponential stability of the scheme is also
considered while it is impossible for truncated Milstein method introduced in
Guo(2018). Three numerical experiments are offered to support our conclusions.
