This paper introduces a bottom-up update mechanism together with a non-recursive initial update procedure that reduces the required extra memory space and computational overhead. A new type of tree is defined based on a different geometrical interpretation of Complete Binary Trees. The new approach paves the way for a special and practical initialization of the tree, which is a prerequisite for an implementation of unilateral update operation. The details of this special initialization and the full update procedures are given for Complete Binary Trees. In addition, a comparison is made between the introduced update method and the bilateral update methods in terms of different performance related metrics.