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The design of a residual dispersion compensating fiber in an equiangular spiral photonic crystal fiber (ES-PCF) structure is presented in the wavelength range 1350-1650 nm. A step-by-step design optimization is demonstrated and a maximum optimized value of average dispersion - 393 ps/nm km with a flattened dispersion profile with a very high birefringence is reported. It has been found that for the ES-PCF, a very high birefringence of 0.0278 at the wavelength 1550 nm can be obtained by employing an elliptical air hole as defect in the core region. An efficient full-vectorial finite-element method with vector edge element is employed in this study. The proposed ES-PCF can be an excellent candidate to be used in a wavelength-division-multiplexing optical fiber transmission system for residual chromatic dispersion compensation as well as maintaining single polarization.