I agree that you should speak to a lawyer and my sense of what you are describing is a substance over form matter that could get you into trouble. While a person without work authorization can start a company in the U.S. (even a foreign person can do this), you CANNOT work for the entity. Without knowing any of the facts, my first impression is that it would be questionable to set up an entity while living here, hire someone and not manage the business.
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I agree with my colleagues. H-4 visa is to accompany or follow to join H-1B. H-4(s) are not authorized to work. When you say "start business" what exactly will be your role? Consult with a competent immigration attorney to ensure that you do not violate the terms of your visa.
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I agree with Attorney Scott: You can form a company, but you cannot work for it.
As a business lawyer, I have helped dozens of foreign clients start businesses in the US, and I have blogged extensively about the challenges that they face. I recommend that you start with the post at the link below.
This information does not constitute legal advice and does not establish an attorney-client relationship.