This note introduces a new algorithmic approach to the problem of checking the property of intransitive noninterference (INI) using discrete-event systems (DESs) tools and concepts. INI property is widely used in formal verification of security problems in computer systems and protocols. The approach consists of two phases: First, a new property called iP-observability (observability based on a purge function) is introduced to capture INI. We prove that a system satisfies INI if and only if it is iP-observable. Second, a relation between iP-observability and P-observability (observability as used in DES) is established by transforming the automaton modeling a system/protocol into an automaton where P-observability (and, hence, iP-observability) can be determined. This allows us to check INI by checking P-observability, which can be done efficiently. Our approach can be used for all systems/protocols with three domains or levels, which is sufficient for most noninterference problems for cryptographic protocols and systems.