AutoMed is a database integration system that is designed to support the integration of schemas expressed in a variety of high-level conceptual modelling languages. It is based on the idea of expressing transformations of schemas as a sequence of primitive transformation steps, each of which is a bi-directional mapping between schemas. To become an efficient schema integration system in practice, where the number and size of schemas involved in the integration may be very large, the amount of time spent on the evaluation of transformations must be reduced to a minimal level. It is also important that the integrity of a set of transformations is maintained during the process of transformation optimisation. This paper discusses a new representation of schema transformations which facilitates the verification of the well-formedness of transformation sequences, and the optimisation of transformation sequences.