  In this paper we study the Loewy structure of the center $ZB$ of a block of a
finite group with respect to an algebraically closed field of prime
characteristic. We first state a new method for calculating the Loewy length
$LL(ZB)$ of $ZB$ in terms of subsections and lower defect groups. By applying
this result we give an upper bound of $LL(ZB)$ which depends on the exponent of
a defect group of $B$ for some cases.
