new lease or amend old one

[Jacob Sharp]

I have 2 tenants on a lease for one of my properties.  One of the tenants is moving out.  Someone else is moving in to take her place.  Current tenants are on a month to month lease.  New tenant will only be there for a short time (3-4 months).  

Should I sign a whole new lease withe remaining tenant and the new tenant?  Can I just produce an amendment and have all of the parties sign the amendment that essentially states the old tenant is moving out and the new tenant is taking her place on the original lease?

Any input would be great!

Thanks!