We are developing searching algorithms for weighted strings such as protein sequences. Let${sum}$ be an alphabet and for each $a{in}{sum}$ its weight ${mu}(a)$ is given. Given a string $A=a_1a_2…a_n; with each ai{in}{sum}$, a substring<$A(i.j)=a_ia_{i+1}…a_j$ has weight ${in}(A(i.j))={in}(a_i)+{in}(a_i+1)+…+{in}(a_j)$.The problem we are dealing with is to preprocess A to build a searching structure, and later, given a query weight M, the structure is used to answer the question of whether there is a substring A(i,j) such that$M={in}(A(i,j))$.In this paper an algorithm that improves over the previous result will be presented. The previously best known algorithm answers a query in $0(frac{nlog;logn}{log; n})$time using a searching structure that requires O(n) amount of memory. Our algorithm reduces the memory requirement to $0(frac{n}{log; n})$ while achieving the same query answer time.