We propose a new methodology to estimate λ, the parameter of the Box-Cox transformation, as well as an alternative method to determine plausible values for it. The former is accomplished by defining a grid of values for λ and further perform a normality test on the λ -transformed data. The optimum value of λ, say λ * , is such that the p-value from the normality test is the highest. The set of plausible values is determined using the inverse probability method after plotting the p-values against the values of λ on the grid. Our methodology is illustrated with two real-world data sets. Furthermore, a simulation study suggests that our method improves the symmetry, kurtosis and, hence, the normality of data, making it a feasible alternative to the traditional Box-Cox transformation.