In this paper an algorithm with guaranteed accuracy is developed for the SISO H₂ optimal tracking problem for a step reference signal. The algorithm utilizes a computer algebra system and interval arithmetic for the achievement of a stringent requirement of guaranteed accuracy. It also makes use of some strucural properties of the solution to the problem in order to facilitate guaranteed accuracy computation. This paper first derives a general expression for the solution to the SISO H₂ tracking problem, revealing some features of the solution useful for guaranteed accuracy computation. Then a guaranteed accuracy algorithm which computes the optimal cost and the controller that accomplishes it is developed by exploiting the features along with some tools for guaranteed accuracy computation. Numerical examples are used to demonstrate the algorithm.