We developed a method, called RNA Assembler using Secondary Structure Information Effectively (RASSIE), for predicting RNA tertiary structures using known secondary structure information. We attempted a fragment assembly-based method that uses a secondary structure-based fragment library. For several typical target structures such as stem-loops, bulge-loops, and 2-way junctions, our method provided numerous good quality candidate structures in less computational time than previously proposed methods. By using a high-resolution potential energy function, we were able to select good predicted structures from candidate structures. This method of efficient conformational search and detailed structure evaluation using high-resolution potential is potentially useful for the tertiary structure prediction of RNA.