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The stable symmetric family of distribution functions (DF’s) suggested by [1] is a family that contains the reverse of every DF belonging to it. It is revealed that the stable families are capable of describing many types of statistical data. We introduce a new stable family via a mixture of the skew-normal distribution and its reverse, after inserting a scale parameter and its reciprocal to the skew-normal distribution and its reverse, respectively. We show that this family contains all the possible types of DFs. Besides, it has a very remarkable wide range of the indices of skewness and kurtosis. Computational technique using EM algorithm is implemented for estimating the model parameters. Moreover, an application with a real data set is presented.

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