The author describes a method involving continued fractions for determining certain real quadratic fields to be of class number one. The method is in fact related to some ideas of H. Lu [Sci. Sin. 24, 1352–1357 (1981; Zbl 0495.12004)], and leads to a different proof of some results of S. Louboutin [J. Number Theory 30, 167–176 (1988; Zbl 0652.12002)].