The COHF algorithm solves block tridiagonal systems of equations by solving a series of systems each the size of one block. If the block dimension of the original system is 2k+1—1 then (k+ 1)2ksystems must be solved. It is shown that this number can be reduced to 3.2k— k — 2. The principle application of this scheme is in the solution of equations derived from elliptic partial differential equations on irregular regions.