The magnetic hyperfine field (mhf) acting on a probe dilutely substituted at the non-magnetic transition element site has been investigated for the pseudo-quaternary Heusler alloys , , , and with and 0.8 by TDPAC measurements utilizing the 133 - 482 keV gamma - gamma cascade in following the -decay of . Magnetization measurements on samples were carried out by using a vibrating-sample magnetometer. The Curie temperature and the saturation magnetization were obtained for each alloy. The lattice parameters of the alloys were determined by x-ray diffraction measurements. The results for the mhf acting on Ta occupying the non-magnetic transition element site are discussed and compared with the mhf systematics for the cobalt-based Heusler alloys.