Facial authentication has the limelight because it has less resistance and it is hard to falsify among various biometric identification. The algorithm of facial authentication can bring about huge difference in accuracy and speed by the algorithm construction. Along with face-extracted data by tracing and extracting pupil, the thesis studied algorithm which extracts data to improve error rate and to accurately authenticate face. It detects face by cascade, selects as significant area, divides the facial area into 4 equal parts to save the coordinate of object. Also, to detect pupil from the eye, the binarization is conducted and it detects pupil by Hough conversion. The core coordinate of detected pupil is saved and calculated to conduct facial authentication through data matching. The thesis studied optimized facial authentication algorithm which accurately calculates facial data with pupil trace.