The ability of analysing and designing an algorithm is quite essential for computer science education. The students in the Analysis and Design of Algorithms (ADA) course are expected to be able to solve problems by choosing one of the proper design methods and to analyse the algorithm's performance in terms of various aspects. Instead of using traditional teaching approaches, a new 4-stage method is proposed to improve the concept of learning and teaching of algorithms. The instructor applied 4 consecutive stages during the tutorials and practical implementations. The students were asked a series of questions for evaluating not only themselves but also the new method and the instructor capability of handling the course by applying the 4-stages. According to the evaluations, the 4-stage method met the course objectives with noticeable rates and the course learning outcomes were achieved with high success rates when compared with the previous semester. In order to attain a sustainable achievement in teaching ADA, it is recommended to apply the 4-stage method every academic year. The application of 4-stages allows the instructor to be more efficient in programming teaching and the student more confident in programming, therefore it can be suggested for other programming related courses.