A characteristic linear equation set is a tridiagonal banded linear equation set with two diagonal points. Generally, it is very difficult to solve the equation set perfectly with methods of linear algebra. Different from the algebra based on LU decomposition and iterative algebra, author brings forward and discusses a solution of the equation set through QR decomposition. QR decomposition is ubiquitous but used few, because of its vast amount of computation. Tridiagonal banded linear equation set with two diagonal points has its characteristic, so QR decomposition can be used to solve the linear equation set with satisfactory precision and economic amount of computation. Analysis and examples are presented to show that the proposed algebra meets the requirements on precision and computation amount in application.