  We show that there is a bijection between the renormalizations and proper
completely invariant closed sets of expanding Lorenz map, which enable us to
distinguish periodic and non-periodic renormalizations. Based on the properties
of periodic orbit of minimal period, the minimal completely invariant closed
set is constructed. Topological characterizations of the renormalizations and
$\alpha$-limit sets are obtained via consecutive renormalizations. Some
properties of periodic renormalizations are collected in Appendix.
