Let P be a set of n points in the plane. A connecting line of P is a line that passes through at least two of its points. A connecting line is called ordinary if it is incident on exactly two points of P. If the points of P are not collinear then such a line exists. In fact, there are Ω(n) such lines [8]. In this note, we present a very simple algorithm for finding an ordinary line, assuming that the points of P are not collinear.