Yes, an h1B visa can be transferred to a new employer.

1. First, get a new job offer
2. Your new employer will file LCA with the Department of Labor.
3. The employer will submit Form I-129 - h1B Transfer Petition to USCIS

The new employer will file Form I-129 petition to USCIS as part of the h1B transfer process. Once USCIS confirm that it has received the form, you can start work