Alternative normalisation to triangular restriction on cointegrating vectors

Johansen recommends that cointegrating vectors must be normalised for inference making purposes. All software packages use triangular normalisation of the cointegrating vectors i.e. the top $r$ by $r$ block of the estimated $\beta$ matrix is an identity matrix. Usually, this is achieved by deriving the row echelon form of the estimated long-run equations (cointegrating equations matrix).

Does any one know of any other normalisation forms? or methods to formulate different normalisation? Thanks

It is also possible to identify the co-integration vectors by imposing restrictions on the adjustment matrix ($\alpha$). This fairly recent overview by Johansen might be useful.