The Navigational Programming (NavP) methodology is based on the principle of self-migrating computations. It is a truly incremental methodology for developing parallel programs: each step represents a functioning program, and each intermediate program is an improvement over its predecessor. The transformations are mechanical and straightforward to apply. We illustrate our methodology in the context of matrix multiplication, showing how the transformations lead from a sequential program to a fully parallel program. The NavP methodology is conducive to new ways of thinking that lead to ease of programming and high performance. Even though our parallel algorithm was derived using a sequence of mechanical transformations, it displays certain performance advantages over the classical handcrafted Gentleman's Algorithm.