The State Merkle tree is used in Ethereum cryptocurrency system to store and verify the current account’s state in a safe and efficient manner. A particular state consists of account balances, the number of transactions, contract codes, and storage values. In this paper, we address the problem of constructing a Merkle tree that minimizes the number of hash values needed for modifying account information based on the transaction distribution to improve system efficiency. The proposed optimization model is a binary quadratic program. Thanks to the exact penalty techniques, it was reformulated as a DC (Difference of Convex functions) program that is effectively solved by the DCA (DC Algorithm). To get a better convex approximation of the objective function without knowledge of a DC decomposition, DCA-Like, a novel extension of DCA, is applied. Additionally, we suggest a combined DCA-Like algorithm and divide-and-conquer algorithm, termed the recursive DCA-Like method, to construct a Merkle tree for a significant amount of the Ethereum accounts. The effectiveness of our approach and its superiority over well-known methods are demonstrated by numerical experiments on several datasets.