Sometimes tantrums are caused by the child's inability to "regulate one's emotions". This can result from the fact that the child is developmentally immature or behind in this area. Can she control herself at school or in other societal environments? If not, then this may the be the cause and you should seek advice from your pediatrician. Just another suggestion/possibility ....
does she have consequences for her actions? What do you do for discipline?
Why does she do it have you asked her what triggers the Tantrums? is there a jealousy issue is the little one getting a lot more than her, especially if she sees the little one throw a tantrum and it works for her. When she does throw a tantrum make her go sit down for a time out and she should stay there, but more than punishment work on the Why she is doing it,