We present a new method for the three-dimensional multivariate decomposition of the MJO into balanced and inertio-gravity (IG) components. The method analyzes global fields with no filtering involved and it provides a quantitative comparison between the contribution of the Rossby, Kelvin and other balanced and IG modes to the MJO circulation and its teleconnections. Results based on the ERA Interim reanalysis data and the multivariate MJO index show that the Rossby mode with the lowest meridional index is the largest contributor to the MJO circulation over the Pacific. A smaller role of the Kelvin mode is diagnosed over the Indian ocean and the maritime continent. The MJO teleconnections in the polar stratosphere appear associated with the leading balanced vertical modes. The presented method shows new ways of evaluating the MJO structure and its global impacts in weather and climate models.