We develop a new method in order to classify the Bianchi I spacetimes
which admit Conformal Killing Vectors (CKVs). The method is based on two
propositions which relate the CKVs of 1 + (n - 1) decomposable
Riemannian spaces with the CKVs of the (n - 1) subspace and show that if
1 + (n - 1) space is conformally flat then the (n - 1) spacetime is
maximally symmetric. The method is used to study the conformal algebra
of the Kasner spacetime and other less known Bianchi type I matter
solutions of General Relativity
