The ranking function method is the main method for the termination analysis of loops, and it indicates that loop programs can be terminated. In view of single-path linear constraint loop programs, this study presents a new method to analyze the termination of the loops. Based on the calculation of the normal space of the increasing function, this method considers the calculation of the ranking function in the original program space as that in the subspace. Experimental results show that the method can effectively verify the termination of most loop programs in the existing literature.