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An improved expression for the prediction of eclipse times in eccentric eclipsing binaries showing apsidal motion is presented. Truncated series expansions have been extended to take into account up to the sixth power of the eccentricity, and all the calculations have been thoroughly checked by means of the Mathematica computer tool. This supersedes the previous equations by Giménez & García-Pelayo (1983). A new description of the process to derive the given equations is made in order to facilitate the verification of the numerous terms involved as well as to correct some misprints which were found in our first paper. Nevertheless, despite some doubts due to the difficulty to check all the terms involved, Equation 20 by Giménez and García-Pelayo (1983) has been confirmed to be free of misprints and, as claimed, was found to be accurate to the fifth power of the eccentricity. This equation has been adopted by many authors in their analysis of apsidal motion elements.
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