The $U(\s)$-algebras are new triple systems, which are obtained 

by extending the concept of Freudenthal-Kantor triple systems 

introduced by I.L. Kantor \cite{k} and K. Yamaguti \cite{y}. 

In this paper, for $U(\s)$-algebras we define the semisimplicity 

and radicals and show that any semisimple $U(\s)$-algebra is 

decomposed into the direct sum of $\s$-simple ideals. We also 

give a formula which describes a relationship between the trace 

form of a semisimple $U(\s)$-algebra $U$ and the Killing form of 

the Lie algebra associated with $U$.