Regards to the state record, that is probably the easiest way to handle it. What is typically done is an LLC interest transfer agreement is prepared so that the units can be properly transferred and liability mitigated regards to the departing member. This is not recorded with the state but is an internal document both parties keep in their records.
I would advise having a lawyer handle it so do not expose yourself unnecessarilly. Most of us here, including myself, offer a free phone consult.
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As usual Frank makes an excellent point. If I were you I'd start by READING what the Operating Agreement says about it. Then I'd have your LLC attorney handle the legalities so that you aren't left with any holdover liability later on. Good Luck.
This is a simple process that can be accomplished effectively with a couple pieces of paper. A quick meeting with your business attorney can facilitate this. As the other answers point out, you should review your operating agreement for withdrawal provisions, and ensure that the company and its members comply with the requirements for changing membership. If you don't have a business attorney you are working with already, I would be happy to refer you to local counsel that could handle this for you without any trouble.
Benjamin Nivison is an attorney licensed to practice law in Washington State. This communication does not create an attorney-client relationship between you and Mr. Nivison, nor does it constitute specific advice for your particular legal matter. The information provided in this communication is for general reference and informational purposes only, and therefore should not be relied on as legal advice. Legal issues are by their nature complex, and any person with a legal question should fully consult with a qualified attorney.