To date in literature, GARCH model has been described not suitable for non-linear foreign exchange series and therefore this paper proposes an Augmented GARCH model that could capture both linear and non-linear behavior of data. The properties of this new model is derived and found to have a minimum variance compared with GARCH model. We employ the use of Brock-Dechert-Scheinkman (BDS) test statistic to confirm the suitability of GARCH model on the data; the new methodology proposed is illustrated with foreign exchange rate data from Great Britain (Pound) and Botswana (Pula) against United States of America (Dollar).