The present invention is directed to a golf ball having a non-planar parting line about non-circular dimples on its spherical surface. The parting line comprises non-concentric arcs having straight connecting line segments between the arcs. Each arc maintains a tangency with its connecting lines and a relief distance greater than or equal to 0.003 inches when measured from an average non-circular dimple diameter to one of the non-concentric arcs and an absolute relief distance of at least 0.001 inches when measured from all points on the non-circular dimple perimeter to one of the non-concentric arcs. The sum of the lengths of the non-concentric arcs relates to the sum of the straight connecting line segments according to the equation: (0.15)ΣLARCS≤ΣLLINES≤(0.50)ΣLARCS.