Tree is a best data structure for data storage and retrieval of data whenever it could be accommodated in the memory. At the same time, this is true only when the tree is height-balanced and lesser depth from the root. In this paper, we propose a sorting based new algorithm to construct the Balanced search tree from Binary Search Tree with minimum of one rotation for the given elements n >14. If the given elements n < 14 then the algorithm automatically constructs the Balanced Search tree without needs any rotations. To maintain the tree in shape and depth, we apply two strategies in the input data. The first one is to apply sorting on the given input data. And the second one is to find the multiples of two positions on the sorted input data. Then, we compare the 3 positions of multiples of two and rewrite it by descending order and repeat this for the entire elements and the rest of the positions also on the sorted data. After, a new input data is formed. Then construct the Binary search tree on the given input data. At last, we will find the output as; a height balanced BST (AVL) with lesser depth from the root for the smaller data such as N < 14, for the greater element N >14 , it requires one rotation from the BST., and the search cost is minimum as possible. In this paper, few case studies have been carried out and analyzed in terms of height and space requirement. Hence, the height of the output BST, normally obtain by maximum height as N/2 or (N/2) – 3.