In many flavors of the nowadays address translators, real addresses are assigned to private hosts without preserving uniqueness; the same real address can be shared among multiple private hosts and the same private host can also obtain different addresses over the time as well. As a result the addresses used for private hosts reflect some kind of ambiguity on those hosts. This proposal introduces the IDNAT model as a solution for that address ambiguity problem. This solution concentrates on defining another virtual identity to identify private hosts in replacement of the ambiguous assigned real IP address. Through agile practices this identity can be assigned to each of the private hosts, and the hosts themselves will be aware of their assigned Ids which are going to be quite unique throughout the private region as well as the entire Internet realm. Moreover, the new Id will play a centric role in the packets transmission so as to identify the private host outside the private region and hence defeating the undesired ambiguity.