We have mapped the CO J = 2 → 1 and J = 1 → 0 emission of the circumstellar envelope of Mira. Emission in both transitions extends to a distance of ~ 4 x 1016cm from the star. In the inner 2 x 1016cm the lines show the presence of three velocity components. The main component has the intermediate velocity and extends over the whole envelope. From this component we have estimated a mass loss rate of 3 x 107 M ⊙ yr -1 and a total molecular mass of 1.2 x 10-3 M⊙. We have shown that, from our data, the only reliable explanation for the lowest and highest velocity components is that they are due to an outflow located within the envelope.