Buying out a business partner is a complicated process. This guide outlines the essential procedures for buying a stake from a business partner.These include creating the motivation behind the buyout. Buying out a business partner can be done in several ways. A partnership buyout agreement lets you plan what will happen when a partner leaves the business. My business partner is retiring and has asked that I buy her out. I am fine with her asking price and terms but she said something that has me baffled. Research the Value of Your Partner's Stake. To reach a fair buyout agreement, you must understand your partner's stake in the business. The final stage of the buyout process involves completing all necessary legal paperwork and ensuring that the transition is smooth and amicable.