Abstract: The well-known Chaikin algorithm generates uniform quadratic B-spline curves by repeating the process of cutting off the corners of a polygon. One disadvantage of this algorithm is the incapability of generating circles. This paper proposes a modification of this algorithm to produce piecewise rational curves; in particular a circle is produced from a given square. For a general control polygon, every two subsequent polygon legs of equal length will correspond to a circular arc. Such an arc will be parameterized by arc length and will remain circular under affine transformations. Both properties are not shared by the standard rational quadratic form.