In this paper, we introduce the concepts of Stone elements, central elements and
Birkhoof central elements of a double MS-algebra and study their related properties.
We observe that the center C(L) of a double MS -algebra L is precisely the Birkhoof
center BC(L) of L. A complete description of factor congruences on a double
MS-algebra is given by means of the central elements. A characterization of balanced
factor congruences of double MS-algebra is obtained. A one-to-one correspondence
between the class of all balanced factor congruences of a double MS-algebra L and the
central elements of L is obtained.