This paper proposes an omnibus test for univariate and multivariate normality based on skewness and kurtosis, using a transformation method from Shenton and Bowman (1977). The test is simple to implement and controls well for size. A multivariate version is introduced, and its size and power are compared with four other multivariate normality tests. The alternative hypothesis in the power simulations is the entire Johnson system of distributions. The univariate test uses transformed skewness and kurtosis to approximate standard normality, resulting in a test statistic approximately distributed as a chi-squared distribution with two degrees of freedom. The multivariate test transforms data to approximate independent standard normals, then applies the univariate test to each dimension. The test statistic is approximately distributed as a chi-squared distribution with 2p degrees of freedom. The paper compares the proposed tests with four other multivariate tests, including Mardia's test, a test based on the correlation between the normalized diagonal of a matrix and jackknifed estimates of its variance, and the multivariate Shapiro-Wilk test. The results show that the proposed test has good size and power properties, particularly against the Johnson system of distributions. The paper also discusses the use of the test in practice, including its application to regression residuals and time series models. Numerical examples are provided, and the test is shown to be effective in detecting non-normality in data, particularly in the case of petal width in the iris dataset. The paper concludes that the proposed test is the preferred test among those considered, as it is simple, has correct size, and good power properties.This paper proposes an omnibus test for univariate and multivariate normality based on skewness and kurtosis, using a transformation method from Shenton and Bowman (1977). The test is simple to implement and controls well for size. A multivariate version is introduced, and its size and power are compared with four other multivariate normality tests. The alternative hypothesis in the power simulations is the entire Johnson system of distributions. The univariate test uses transformed skewness and kurtosis to approximate standard normality, resulting in a test statistic approximately distributed as a chi-squared distribution with two degrees of freedom. The multivariate test transforms data to approximate independent standard normals, then applies the univariate test to each dimension. The test statistic is approximately distributed as a chi-squared distribution with 2p degrees of freedom. The paper compares the proposed tests with four other multivariate tests, including Mardia's test, a test based on the correlation between the normalized diagonal of a matrix and jackknifed estimates of its variance, and the multivariate Shapiro-Wilk test. The results show that the proposed test has good size and power properties, particularly against the Johnson system of distributions. The paper also discusses the use of the test in practice, including its application to regression residuals and time series models. Numerical examples are provided, and the test is shown to be effective in detecting non-normality in data, particularly in the case of petal width in the iris dataset. The paper concludes that the proposed test is the preferred test among those considered, as it is simple, has correct size, and good power properties.