  Normal copula with a correlation coefficient between $-1$ and $1$ is tail
independent and so it severely underestimates extreme probabilities. By letting
the correlation coefficient in a normal copula depend on the sample size,
H\"usler and Reiss (1989) showed that the tail can become asymptotically
dependent. In this paper, we extend this result by deriving the limit of the
normalized maximum of $n$ independent observations, where the $i$-th
observation follows from a normal copula with its correlation coefficient being
either a parametric or a nonparametric function of $i/n$. Furthermore, both
parametric and nonparametric inference for this unknown function are studied,
which can be employed to test the condition in H\"usler and Reiss (1989). A
simulation study and real data analysis are presented too.
