In this paper, we introduce a new approach to compute the partial fraction decompositions of rational functions and describe the results of its trials at three secondary schools in Hong Kong. The data were collected via quizzes, questionnaire and interviews. In general, according to the responses from the teachers and students concerned, this new approach has potential to be introduced at the senior secondary level, as an alternative to the method of undetermined coefficients described in common secondary mathematics textbooks. Some remarks on the related pedagogical issues are included.[Copyright of International Journal for Mathematics Teaching and Learning is the property of University of Exeter / Centre for Innovation in Mathematics Teaching.Access via Directory of Open Access Journals: http://www.cimt.plymouth.ac.uk/journal/default.htm]