The author has been prompted to write this article about finger multiplication for a number of reasons. Firstly there are a number of related articles in past issues of "Mathematics Teaching" ("MT") which have connections to this algorithm. Secondly, very few of his primary teaching students and professional colleagues appear to be aware of the algorithm and yet, upon introduction to it, most of them express surprise, delight and some interest as to why it works. The third reason is that, in seeking to explain it, opportunities arise to represent the algorithm in alternative practical and diagrammatic forms leading to an algebraic explanation which is appropriate, in the author's opinion, for students aiming for the higher GCSE mathematics grades or for those studying A level mathematics. However, students of all abilities should be able to appreciate, and gain from, the practical elements of the exercise even if the algebraic element is not fully understood. In this article, the author presents an interesting algorithm. (Contains 6 pictures.)