The paper investigates the role of suprathermal particles (He++) in the propagation of low-frequency waves in average magnetosheath plasma by utilizing a model which is a concatenation of two magnetohydrodynamic (MHD) fluids. The suprathermal component is described by a relativistic, collisionless anisotropic fluid while the background plasma is assumed to be a nonrelativistic, anisotropic MHD fluid. The pressure components of both the fluids are described by heuristic double-polytropic laws which are fairly well supported by observational data. The linearized analysis is carried out and dispersion relation is derived using normal mode technique. It is found that inclusion of the suprathermal component causes the excitation of an additional mode of propagation, besides reducing the phase speeds of slow, fast, and Alfv¿n modes. The additional mode, which can be characterized as a hybrid of the suprathermal and the fast modes in the direction perpendicular to the magnetic field, is the only mode which transports energy in the direction perpendicular to the magnetic field. Using appropriate polytropic indices obtained from AMPTE/IRM measurements in the magnetosheath leads to a new ordering of phase speeds and density-magnetic field correlation of the fast mode. The new suprathermal mode shows positive density-magnetic field correlation.