Yaron Sella recently proposed a scalable version of Jakobsson's algorithm to traverse a hash chain of size n. Given the hash chain and a computation limit m (k=m+1 and (b = $\sqrt[k]{n}$)), Sella's algorithm traverses the hash chain using a total of kb memory. We improve the memory usage to k(b–1). Because efficient hash chain traversal algorithms are aimed at devices with severely restricted computation and memory requirements, a reduction by a factor of (b–1)/b is considered to be important. Further, our algorithm matches the memory requirements of Jakobsson's algorithm while still remaining scalable. Sella's algorithm, when scaled to the case of Jakobsson's algorithm, has a memory requirement of about twice that of Jakobsson's.