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, Husler 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 Husler and Reiss (1989). A simulation study and real data analysis are presented too.
