A new lattice reduction method is introduced to solve the problem of integer ambiguity resolution in UNSS carrier phase precise positioning. The current LLL reduction algorithm is improved based on a orthogonal Householder transformation with systematic rotation. The comparative range is extended to n. The reduction base vectors are preordered and a HE-LLL reduction algorithm is proposed. Experiments with different time intervals and baseline lengths were executed and a comparison was made between the HE-LLL algorithm and other algorithm concerning condition number，non-or-thogonalindex，reduction time，and changing trend of the length of orthogonal row vector. The recults show that the HE-LLL algorithm has improved reduction efficiency，and can well restrict the length of orthogonal row vector.