<p>Testing the association of two high-dimensional random vectors is of fundamental importance in the statistical theory and applications. In this paper, we propose a new test statistic based on the Frobenius norm and subtracting bias technique, which is generally applicable to high-dimensional data without restricting the distributional Assumptions. The limiting null distribution of the proposed test is shown to be a random variable combining a finite chi-squared-type mixture with a normal approximation. Our proposed test method can also be a normal approximation or a finite chi-squared-type mixtures under additional regularity conditions. To make the test statistic applicable, we introduce a wild bootstrap method and demonstrate its validity. The finite-sample performance of the proposed test via Monte Carlo simulations reveals that it performs better at controlling the empirical size than some existing tests, even when the normal approximation is invalid. Real data analysis is devoted to illustrating the proposed test.</p>