The Unbiased Forward Rate Hypothesis (UFRH) stipulates that the forward rates should be a perfect predictor for the future spot rates. A number of studies have tested the UFRH and foreign market efficiency and concluded that the hypothesis does not hold. This phenomenon is known as the UFRH puzzle. A number of studies that reject the UFRH have made use of ordinary least square (OLS) methods and support a linear adjustment between spot and forward exchange rates. This paper establishes that the use of a linear model in testing the UFRH can lead to a misspecification problem if indeed there is a nonlinear adjustment between the forward and spot exchange rates. In order to overcome the problem of model misspecification, this paper applies the nonlinear method of the class of the Smooth Transition Regression (STR) model in assessing the relationship between the Rand-US Dollar future spot and forward exchange rates. With the aid of a series of diagnostic tests, the paper shows that there is indeed a nonlinear adjustment process between the Rand-US Dollar spot and forward exchange rates and that there exists a regime in the STR model where the UFRH eventually holds. Furthermore, the out-of-sample forecast results show that the STR forecasting method outperforms the OLS and random walk methods in forecasting the future spot exchange rate.