If you are saying it: use "He is the friend of Taro." If you wish to talk like a native speaker we would just say "He is Taro's friend." Just say "He is Taro's friend." There is no need to make it complicated.

But you can also say "He is the friend of Taro's that we were talking about." or you could write * He was the friend of Taro that we were talking about. * The latter does not have a clear implication that they remain friends or that the subject is still living.

Did you mean "Joe is A friend of Taro's" and "Joe is A friend of Taro"? If you did, here are a few ideas to share with you: 1. Both sentences are "correct." 2. The one with 's is called a DOUBLE POSSESSIVE. (Please check the Web for many, many explanations.) 3. Although many of us native speakers cannot explain it, we use it. 4. Sometimes the one WITHOUT 's means that maybe Taro does not know that Joe has friendly feelings toward him. That is, maybe Joe and Taro have never spoken, but Joe -- for some reason -- likes Taro. If anyone says anything bad about Taro, Joe will say, "Don't say that. I like Taro." 5. The MOST IMPORTANT thing to remember: You MUST use the possessive if you use the PROnoun: Joe: I am a friend of Taro./ I am a friend of Taro's. Mona: Really? Well, I am a friend of HIS, too. (You canNOT say "him" or "he.") Joe: Are you also a friend of Maria? / Are you also a friend of Maria's? Mona: No, I am not a friend of HERS. ***** Sometimes there IS a big difference: This is a photograph of Taro. = Someone took a photograph of Taro. This is a photograph of Taro's. = Taro owns this photograph (maybe the photograph shows only Mona).

I agree with Randy, if you were going to use number one you would change it to, "He is Taro's friend." Like that they both mean the same thing.

Number one is not correct. It is mistaken to attempt to indicate possession twice.