Parenting GameObject to another animated GameObject

What's the best way to parent GameObject to anoter animted GameObject? It seems like Unity locks all transforms in the hierarchy of the animated object. I'll give you an example of what I'm talking about: 1) Parent object A to animated object B via SetParent(Transform). Everything is ok, object A keeps its global scale 2) On LateUpdate() parent object A to another non-animted object. Expected behaviour - object A keeps its global scale, real behaviour - object A keeps its localScale therefore modifying its global scale and in my case becomes smaller and smaller with each reparenting. Thanks in advance.