Context. High-velocity halo stars provide important information about the properties of the extreme Galactic halo. The study of Population II unbound and bound stars enables us better estimate the mass of the halo. Aims. We carried out a detailed spectroscopic and kinematic study of two red horizontal branch stars, CD-41 15048 and HD 214362. Methods. The atmospheric parameters, chemical abundances, and kinematical properties were determined using high-resolution optical spectroscopy and employing the local thermodynamic equilibrium model atmospheres of Kurucz and the spectral analysis code moog. Results. We found that CD-41 15048 and HD 214362 are metal-poor red horizontal branch stars. Their abundance patterns are similar to other metal-poor halo stars already investigated. Our kinematic analysis of the 3D space motions shows that HD 214362 has a highly eccentric (e = 0:95) orbit and passes at 2 kpc from the Galactic center. CD-41 15048, for an adopted distance of 1.3 kpc, has an extreme retrograde motion and travels with very high velocity relative to the Galactocentric reference frame (VGRF = 583 km s 1 ). Conclusions. CD-41 15048 is a bound or an unbound star, depending on the adopted Galactic potential. We also show that the red horizontal branch star BD+09 3223 is another example of a hypervelocity star. Whether it is bound or unbound to the Galaxy depends on the assumed mass and adopted Galactic potential. Possible origins of these two high-velocity stars are briefly discussed. CD-41 15048 and BD+09 3223 are further examples of evolved stars to join the restricted group of hypervelocity stars. Finally, our results seem to contradict the idea that a passage of a star very close to the Galactic center is the only possible origin of hypervelocity stars.