It can't be new information if it already existed. I'm talking about recombinants, which are rearrangements of already existing genetic information.
The old information is destroyed, and new information created, by re-organization.
This is designed variation. It is why we have different colored eyes, skin, and hair. Why finches have different sized beaks. It is why we have different breeds of cats, dogs, birds, etc.
You mean on two different strands of DNA, or do you mean the shuffling of genes during meiosis?