This paper develops a convergence model of the term structure of interest rates in context of entering the European Monetary Union (EMU). Compared to other models developed so far in this field, our model specification ensures convergence of the domestic short-term interest rates to the euro area ones. We achieve this convergence by stating that the spread between domestic and euro short-term interest rate follows the Brownian bridge process. We also develop an econometric counterpart of the theoretical model. To tackle the problem of nonstationarity and nonlinearity of the model, we apply the extended Kalman filter for coefficient estimation.