Pinch analysis is a methodology used for minimizing energy and material consumption in engineering processes. It features the identification of the pinch point and minimum external resources. Two common established approaches are used to identify these features: the graphical approach and the algebraic method, which are time-consuming and susceptible to human and calculation errors when used for a large number of process streams. This paper presents an algorithmic procedure to heat integration based on the algebraic approach. The algorithmic procedure is explained in a didactical manner to introduce pinch analysis for students and novice researchers in the field. Matlab code is presented, which is also intended for developing a Matlab toolbox for process integration.