In this paper, we examine the monetary model of the Malawi Kwacha - U.S. dollar exchange rate during the current floating exchange rate system by applying several recent developments in the econometrics of unit roots and cointegration. Several interesting and important results are found. A single cointegration equation is identified whose coefficients conform to the restriction implied by the monetary model. The short run equation indicates the following results: First, the domestic interest rate has a negative sign, which indicates that increases in the domestic interest rate lead to an appreciation of the Malawi Kwacha. Domestic money supply has a positive sign, which implies that reductions in domestic money supply lead to an appreciation of the Malawi Kwacha. These results have led to the following conclusions. First, we have demonstrated through the use of Johansen's multivariate cointegration technique that an unrestricted monetary model does provide a valid explanation of the long-run nominal Malawi Kwacha - US dollar exchange rate, thus lending support to the interpretation of the model as describing a long run equilibrium relationship. Second, money supply can be employed as a tool to influence the exchange rate. This arises because a reduction in the nominal money supply through open market operations raises domestic rate of interest rate for given money demand in the short run. The increase in domestic interest rate results in an incipient short-term capital inflow. This causes the exchange rate to appreciate. Finally, the correct sign and significance of the foreign country interest rate signify the role of currency market liberalization and it is a justification of our choice of RSA as Malawi's major trading partner in our model.