The quality of edge detection is related to detection angle, scale, and threshold. There have been many algorithms to promote edge detection quality by some rules about detection angles. However these algorithm did not form rules to detect edges at an arbitrary angle, therefore they just used different number of angles and did not indicate optimized number of angles. In this paper, a novel edge detection algorithm is proposed to detect edges at arbitrary angles and optimized number of angles in the algorithm is introduced. The algorithm combines singularity detection with Gaussian wavelet transform and edge detection at arbitrary directions and contain five steps: 1) An image is divided into some pixel lines at certain angle in the range from 45° to 90° according to decomposition rules of this paper. 2) Singularities of pixel lines are detected and form an edge image at the certain angle. 3) Many edge images at different angles form a final edge images. 4) Detection angles in the range from 45° to 90° are extended to range from 0° to 360°. 5) Optimized number of angles for the algorithm is proposed. Then the algorithm with optimized number of angles shows better performances.