Static Single Assignment (SSA) intermediate representation is widely used to optimize and compile code in imperative and object-oriented languages, but it can also be useful for static type analysis. We introduce FJSSA , a Java-like imperative calculus supporting programs in SSA form; we define its big-step operational semantics, and a judgment to statically check whether a program is in SSA form, and prove its soundness. FJSSA provides a formal basis for type analysis of programs in SSA form in object-oriented languages.