Based on the general singular value decompositions of quaternion matrices, a relationship of the singular values and singular vectors was given between the generalized extended quaternion matrix of symmetric rows or columns and its original quaternion matrix, which extends the existing results. Theoretical predictions and numerical evidences show that, for a class of extended matrices, the singular value decomposition using the original quaternion matrix rather than the generalized extended quaternion matrix can save dramatically the memory and alleviate considerably the computational burden without loss of any numerical precision.