This paper describes a method of obtaining a surface region of triangular shape surrounded by usual regular surface derived from a spline net. The element patch is of degree two and the connection of patches is C¹. Each patch is defined by Bézier control points. The surrounding region is defined by spline net of degree two with arbitrary knot distance ratios. At first we introduce a closed surface with minimum number of usual Bézier patches of degree two to show an application of the method and its quality of the connection. Then we treat rounding of a convex region connected with a regular spline surface of degree two with the equal knot distance ratios. From disposition of control points of the surrounding spline net, we give the locations of Bézier control points of the central three patches which connect with each other as well as with the surrounding patches in C¹. Then the method is extended to a case of arbitrary knot distance ratios. Examples are also shown. Because of practical uses, we restricted the connection to the lowest degree curved surfaces, the method is applicable to the higher degree patches as well in C¹ connection.