Several modifications of the Laplace distribution have been introduced and applied in various fields up to this day. In this paper, we introduce a modified symmetric version of the classical Laplace distribution. We provide a comprehensive theoretical description of this distribution. In particular, we derive the formulas for the $k$th moment, quantiles and several useful alternative representations of the distribution. We derive the maximum likelihood estimators of the parameters and investigate their properties via simulation. Finally, we analyse three real-world datasets to illustrate the usefulness of the modified classical Laplace distribution. The results suggest that further improvement to classical Laplace distribution fitting is possible and the new model provides an attractive alternative to the classical Laplace distribution.