In this paper, we introduce the notion of BH-algebras with condition (S) and
we show that a BCH-algebra $X$ with the additional identity 
$(x*y)*z=x*(y*(0*z))$ for all $x,y,z\in X$ 
is a BCH-algebra with condition (S). Next, we further discuss the structure 
of ideals in BH-algebra using $A(x,y)$.