The quantitative analysis of shapes is required in some research fields, such as taxonomy, agronomy, ecology, medicine, among others. The quantification of an object shape, or a biological entity shape as extension, is usually performed on its closed contour data. Normally, the closed contours are automatically extracted from digital images. In these fields, the most used contour descriptors are the Elliptical Fourier Descriptors (EFD). In this paper we propose a new contour descriptor based on the Discrete Hartley Transform (DHT) that uses only half of the coefficients required by EFD to obtain a contour approximation with similar error measure. The proposed closed contour descriptors provide an excellent capability of contour information compression being suitable to be applied as input parameters of any shape classifier. The proposed parameterization can represent all kinds of closed curves and also it has the advantage that both the parameterization and the reconstructed shape from a reduced amount of them can be computed very efficiently by the fast Discrete Hartley Transform (DHT) algorithm.