For reliable storage services, we need a way not only to monitor the state of stored data but also to recover the original data when some data loss is discovered. To solve the problem, a novel technique called HAIL has been proposed. Unfortunately, HAIL cannot support dynamic data which is changed according to users' modification queries. There are many applications where dynamic data are used. So, we need a way to support dynamic data in cloud services to use cloud storage system for various applications. In this paper, we propose a new technique that can support the use of dynamic data in cloud storage systems. For dynamic data update, we design a new data chunk generation strategy which guarantee efficient data insertion, deletion, and modification. Our technique requires O(1) operations for each data update when existing techniques require O(n) operations where n is the size of data.