  Conditions are found which ensure that local boost invariance (LBI),
invariance under a linear boost isotropy, implies local boost symmetry (LBS),
i.e. the existence of a local group of motions such that for every point $P$ in
a neighbourhood there is a boost leaving $P$ fixed. It is shown that for Petrov
type D spacetimes this requires LBI of the Riemann tensor and its first
derivative. That is also true for most conformally flat spacetimes, but those
with Ricci tensors of Segre type [1(11,1)] may require LBI of the first three
derivatives of curvature to ensure LBS.
