This is banking application,so that customer need to login different userid at the same time.
What is the use case?
In my opinion, relying on IE's inprivate browsing / chrome's incognito mode / firefox's whatever-it's-called for correct behaviour is bad both from usability and from security aspects.
Most users won't be so browser savvy as to know how these work under the hood. For most, a new window is a new window, regardless of whether it's opened using Ctrl+N or from start menu or Ctrl+shift+N, and they expect them all to behave the same.
There some good info here. The standard answer though is that it is not possible (not without a lot of hacks, at least). You case may be more relaxed (intranet app, limited users) and you maybe have some liberty to make assumptions.
Still that's not the way web browsers were supposed to function, its a bad requirement....