The demand for processing vast volumes of data has surged dramatically due to the advancement of machine learning technology. Large-scale data processing necessitates substantial computational resources, prompting individuals and enterprises to turn to cloud services. Accompanying this trend is a growing concern regarding data leakage and misuse. Homomorphic encryption (HE) is one solution for safeguarding data privacy, enabling encrypted data to be processed securely in the cloud. However, the encryption and decryption routines of some HE schemes require considerable computational resources, presenting non-trivial work for clients. In this paper, we propose an outsourced decryption protocol for the prevailing RLWE-based fully homomorphic encryption schemes. The protocol splits the original decryption into two routines, with the computationally intensive part executed remotely by the cloud. Its security relies on an invariant of the NTRU-search problem with a newly designed blinding key distribution. Cryptographic analyses are conducted to configure protocol parameters across varying security levels. Our experiments demonstrate that the proposed protocol achieves up to a $67\%$ acceleration in the client's local decryption, accompanied by a $50\%$ reduction in space usage.