We consider here a three-parameter generalization of the skew-normal distribution, denoted by GSN (), defined through a standard trivariate normal distribution with correlationmatrix Σ, which is a special case of the unified multivariate skew-normal distribution studied by Arellano-Valle and Azzalini (2006). We then present some simple properties of this distribution and derive its moment generating function. Next we show that distribution of order statistics from the four variate normal distribution is mixtures of these generalized skew-normal distributions.