In this paper, we propose a novel construction for a symmetric encryption scheme, referred as SEBQ which is built on the structure of quasigroup. Utilizing the concepts of chaining like mode of operation, SEBQ is a block cipher with various in-built properties. This scheme is proven to be resistant against chosen plaintext attack (CPA) and on applying unbalanced Feistel transformation [18], it achieves security against chosen ciphertext attacks (CCA). Subsequently, assessment has been conducted for the randomness of this scheme by running the NIST Statistical test suite be analysing the impact of change in the secret key and plaintext on ciphertext through an avalanche effect analysis. Thereafter, a comparative analysis has been done referring the results with existing schemes based on quasigroups [8,40]. Moreover, we also analyse the computational complexity in terms of number of operations needed for encryption and decryption.