Higher-order boundary element method (HOBEM) for wave diffraction/radiation analysis is a powerful tool for its applicability to a general (curved) geometry. Inspired by the paper which examined the convergence of BIE code with constant panels (Martic, et al., 2018; OMAE2018-77999), the convergence characteristics of HOBEM with quadrilateral panels have been examined. Here, the effect of removal of irregular frequencies is particularly focused as discussed by Martic, et al. (2018). The irregular frequency removal has been made by the rigid-lid method which is applicable to HOBEM, where the intersection line between the body-surface and the free-surface should be carefully handled. The results show that for first order quantities the convergence is quite good for both cases with/without irregular frequency removal (except where the irregular frequencies affect for the case without irregular frequency removal). For mean drift forces, the convergence becomes poor particularly for the case without irregular frequency removal. The convergence characteristics are examined and some discussions are made.