  In this paper, we first show that the irreducible characters of a quotient
table algebra modulo a normal closed subset can be viewed as the irreducible
characters of the table algebra itself. Furthermore, we define the character
products for table algebras and give a condition in which the products of two
characters are characters. Thereafter, as a main result we state and prove the
Burnside-Brauer Theorem on finite groups for table algebras.
