  The Korkine-Zolotareff (KZ) reduction is one of the often used reduction
strategies for lattice decoding. In this paper, we first investigate some
important properties of KZ reduced matrices. Specifically, we present a linear
upper bound on the Hermit constant which is around $\frac{7}{8}$ times of the
existing sharpest linear upper bound, and an upper bound on the KZ constant
which is {\em polynomially} smaller than the existing sharpest one. We also
propose upper bounds on the lengths of the columns of KZ reduced matrices, and
an upper bound on the orthogonality defect of KZ reduced matrices which are
even {\em polynomially and exponentially} smaller than those of boosted KZ
reduced matrices, respectively. Then, we derive upper bounds on the magnitudes
of the entries of any solution of a shortest vector problem (SVP) when its
basis matrix is LLL reduced. These upper bounds are useful for analyzing the
complexity and understanding numerical stability of the basis expansion in a KZ
reduction algorithm. Finally, we propose a new KZ reduction algorithm by
modifying the commonly used Schnorr-Euchner search strategy for solving SVPs
and the basis expansion method proposed by Zhang {\em et al.} Simulation
results show that the new KZ reduction algorithm is much faster and more
numerically reliable than the KZ reduction algorithm proposed by Zhang {\em et
al.}, especially when the basis matrix is ill conditioned.
