How to transfer H1 form one to

I'm currently working for a company in H1 status, and have got a job offer from another company. There is an H1 transfer between these 2 companies. But, these two companies both have no idea how to do that. I guess the new company should file an H1 application like what the current company I'm working with did before. But, what should the current company do? Should they two talk each? Any one had the experience, please give me some adivces. Thanks a lot!