What is the proper way to deal self plagiarism? Couple of months ago i've checked plagiarism of one of my research work in turnitin.
I've reused the same research work in order enhancement it. When i checked new assignment again in turnitin with different class ID it shows similarity index from old one. I've changed my university and as per its rule it can not accept new assignment with such similarity index. 
How can i deal with this issue?
I'll assume you're wondering why your similarity level is still high.

With most courses, it is up to the professor. You might have a professor that would allow you to do something like this, but it's incredibly unlikely.

When assignments are submitted to TurnItIn, they are stored in an external database that your school unlikely has access to. This is something maintained by the company. This is why your originality checks appeared to remain the same despite transferring institutions. You might have some benefit to this, as your professor's "common sense" is pretty important when using something like TurnItIn; they'll basically have to review it and talk to you about it. However, if it's not random bits and bobs like citations and bibliographies, you might not be in such good graces.

As for what you can do about this, very little. Talk to your professor about re-using the old assignment. They're going to need to know about it regardless. However, my two-cents are that you shouldn't have bothered reusing an old assignment; most professors simply do not accept work that was done for a different course, regardless if it was your work or not. None of mine ever have, from recent memory.