Of course!  COBRA insurance laws are meant to protect people and families  while they seek out other health insurance either through an independent company or by becoming employed elsewhere.  Therefore, you can drop your COBRA health insurance coverage at any time.  You need  to notify your group health insurance provider under COBRA when you would like the coverage to end.   Make sure  to check with your new employer or insurer for when the policy will become active.  In many companies, there is a 90 day waiting period until COBRA insurance kicks in.