In this article we show that the asymptotic iteration method (AIM) allows one to numerically find the quasinormal modes of Schwarzschild and Schwarzschild de Sitter (SdS) black holes. An added benefit of the method is that it can also be used to calculate the Schwarzschild anti-de Sitter (SAdS) quasinormal modes for the case of spin zero perturbations. We also discuss an improved version of the AIM, more suitable for numerical implementation. ¶ Main address from 1st of June. 1 The phrase "continued fraction" used for WKB solutions should not be confused with the type of continued fractions developed from Frobenius series for QNMs by Leaver [2]. In the rest of the paper "continued fraction" will mean those generated from Frobenius series.