This paper presents a new boundary element formulation in which the eigenvalue appears outside the integral operator, which distinguishes it from the Helmholtz integral equation. Thus, the formation of global matrices need only be assembled once. Since the kernel of the operator used in the new formulation is real‐valued, all calculations can be carried out in a much simpler way in the real domain. The complex acoustic pressure amplitude is considered herein to deivate by a certain amount from a harmonic function. It is an important contribution that an exact relation between the deviator and the complex acoustic pressure amplitude is constructed locally and thus no more approximations are introduced except conventional boundary discretizations. Several examples are given to illustrate the feasibility of an accurate, effective prediction of resonance.