When designing a static analysis, choosing between a flowinsensitive or a flow-sensitive analysis often amounts to favor scalability over precision. It is well known than specific program representations can help to reconcile the two objectives at the same time. For example the SSA representation is used in modern compilers to perform a constant propagation analysis flow-insensitively without any loss of precision. This paper proposes a provably correct program transformation that reconciles them for any analysis. We formalize the notion of Flow-Insensitive-Completeness with two collecting semantics and provide a program transformation that permits to analyze a program in a flow insensitive manner without sacrificing the precision we could obtain with a flow sensitive approach.