Anewexact solution of embedding class I is presented for a relativistic anisotropicmassive fluid sphere. The new exact solution satisfies Karmarkar condition, is well-behaved in all respects, and therefore is suitable for the modelling of superdense stars. Consequently, using this solution, we have studied in detail two compact stars, namely, XTE J1739-289 (strange star 1.51$M_{\odot}$, 10.9 km) and PSR J1614-2230 (neutron star 1.97$M_{\odot}$, 14 km). The solution also satisfies all energy conditions with the compactness parameter lying within the Buchdahl limit.
