In recent years, e-learning and b-learning designs for graduate courses have proliferated in the European Higher Education Area. This paper includes the definition for a model for the assessment of the quality of on-line teaching based on an audit by specialised technical personnel who are independent of the design of the teaching materials and which could be a proposal for the higher education quality assurance models of the European Association for Quality Assurance in Higher Education (ENQA). This template would be useful in undergraduate and graduate courses. This model has been applied in external assessments of the on-line teaching given in the Master's Degree in the Diagnosis of the State of Conservation of the Historical Heritage by the Pablo de Olavide University of Seville, in the 2013-2014 academic year, with the purpose of validating the advantages of the method and examining aspects for improvement in accordance with the Deming cycle, also known as the PDCA (Plan-Do-Check-Act) cycle. The instrument developed for the audits includes all the criteria and indicators considered relevant for quality assessment from a pedagogical perspective. The complete tool, developed in-house, is presented in this article as it is believed that it can serve as a model for the assessment of any on-line teaching.