Using the concept of double extension, Benayadi [2] showed how to construct a new quadratic algebra ( g ( A ), T ) given a quadratic algebra ( A, B ). With both algebras and an invertible skew-symmetric algebra D over A , he endowed ( A, B ) with a simplectic structure through a bilinear form ω, obtaining a simplectic algebra ( g ( A ), T , Ω). Our purpose in this short communication is to show the construction given by Benayadi and present the complete development of each one of his assertions. We remark that this communication does not have original results and it was made as a result of the undergraduated work titled Construccion de algebras de Lie simplecticas desde algebras de Poisson cuadraticas[5], which was awarded as the best mathematics under-graduated thesis in the XXVI Contest at Universidad Nacional de Colombia, Sede Bogota. The work was written by the first author under the direction of the second author.