The non-Gaussian quasi maximum likelihood estimator is frequently used in
GARCH models with intension to improve the efficiency of the GARCH parameters.
However, the method is usually inconsistent unless the quasi-likelihood happens
to be the true one. We identify an unknown scale parameter that is critical to
the consistent estimation of non-Gaussian QMLE. As a part of estimating this
unknown parameter, a two-step non-Gaussian QMLE (2SNG-QMLE) is proposed for
estimation the GARCH parameters.