  A conjecture appears in \cite{milsteinscheme}, in the form of a remark, where
it is stated that it is possible to construct, in a specified way, any high
order explicit numerical schemes to approximate the solutions of SDEs with
superlinear coefficients. We answer this conjecture affirmatively for the case
of order 1.5 approximations and show that the suggested methodology works.
Moreover, we explore the case of having H\"{o}lder continuous derivatives for
the diffusion coefficients.
