Tests of normality are far too sensitive. They are almost always significant with real life data, but we know from simuation studies that many statistical procedures are robust to even considerable departures from normality. The statistician George Box likened normality tests before running regression models as like setting out to sea in a rowing boat to see was the sea calm enough to launch an ocean liner.

Multivariate normality greatly increases the likelihood that any test will give a significant departure, and discourage you from using models that would actually have worked. 

Awopeju

Koizumi, Okamoto and Seo in their 2009 paper published in Journal of Statistics: Advances in Theory and Applications, proposed a  (then) new JarqueBera test for assessing multivariate normality by using Mardia’s and Srivastava’s skewness and kurtosis, respectively. The 'new' test statistics were asymptotically distributed as - χ2 distribution. They investigated accuracy of expectations, variances and upper percentage points for multivariate Jarque-Bera tests by Monte Carlo simulation. 

see: http://scientificadvances.co.in/admin/img_data/166/images/[5]%20JSATA%2090702%20Kazuyuki%20Koizumi%20et%20al.%20207-220.pdf

 Robert James

In the paper, it was concluded that "But approximations of expectations, variances and upper percentage points of MJBM and MJBS are not good when the sample size N is small".

The only small sample size used is 20. I think it is not enough to generalize the pattern for small sample size.

Besides, the information given is vital.

As one of answers, you can find in the article entitled

An Omnibus Test for Univariate and Multivariate Normality

by Jurgen A. Doornik1 andHenrik Hansen,

Oxford Bulletin of Economics and Statistics

Volume 70, Issue Supplement s1, pages 927–939, December 2008.

Thank you for your attention.