Marie is correct - this is unlikely to work unless you are VERY careful to not let Google know that the websites are connected, as they're partial to transferring penalties from one site to another if you try to get rid of a penalty by starting a new, identical website. Simply redirecting a penalised site is a trick that used to work back in 2009, 2010 (you don't mention redirection, but it's worth noting that this used to work, so if you see it mentioned online it's probably old information).
Even if you do not redirect the old site, Google may still recognise that the content is identical to a website it previously penalised, especially if all the new site's registration information, hosting, template, etc. is the same as the old site.
That's not for sure - you may get away with doing this if there are no ties between the old, penalised site and the new site, but using identical content is a big give-away.
Assuming that your penalty was links-related, the safest way to do this is to remove the old site's content, wait until Google cache the old site with the content gone (so the content is completely out of the index), take the site down and re-publish on the new domain. That said, Google's ability to remember what it has seen before could result in the scenario Marie describes.