A majority of previous research done on Support Vector Data Description (SVDD), which is one of the excellent and applied widely to kernel methods, were directed toward efficient implementations and practical applications. However, very few research attempts have been directed toward studying the properties of SVDD solutions. In this work, the primal optimization of SVDD is first transformed into a convex constrained optimization problem, and the uniqueness of the centre of ball is proved while the non-uniqueness of the radius is investigated. This paper also investigates the property of the centre and radius from the perspective of the dual optimization problem, and suggests a method to calculate the radius. The results of this paper complete the SVDD theory, and contribute to further theoretical study and extensive applications.