Uh, no. Read up on counterparty risk, credit default swaps, and the crazy interdependencies of financial institutions.
If bank A goes bad, institution B might have sold lots of CDS on bank A, requiring it to pay out more than it is able, so it goes under. Institutions C and D might have sold CDS on institution B, etc.
If bank A goes bad, institution B might have sold lots of CDS on bank A, requiring it to pay out more than it is able, so it goes under. Institutions C and D might have sold CDS on institution B, etc.