Change of employer when on L1B visa and have valid H1B petition

I am currently in US on L1B visa and working for Employer A who has filed my H1B visa. My H1B petition is approved and valid from 1st October 2016. So my question is will I be able to change to employer B using my existing H1b petition without leaving the country using the H1b visa transfer? Are there any issues with that? Also what would be required in that case?

Appreciate your response.