Compositional data, multivariate observations carrying relative information, are popularly expressed in additive logratio coordinates which are easily interpretable as they use one of the components as ratioing part to produce pairwise logratios. These coordinates are however oblique and they lead to issues when applying multivariate methods on them, including widely-used techniques such as principal component analysis and linear regression. In this paper we propose a way to redefine alr coordinates with respect to an orthonormal system and we also extend the idea to the case of compositional tables. The new approach is demonstrated in an application to movement behavior data
