In this work for the first time we give the evidence that compound Dy_{1-x}Y_x Rh_4B_4 with the tetragonal body-centered crystal structure LuRu_4B_4 is the ferrimagnetic at temperatures T_{Cur}<40 K, ferrimagnetic superconductor at T_C <10 K and antiferromagnetic superconductor at T_N <3 K. No reentrant behavior was found down to T = 0.32 K. For the first time by means of a method of microcontact spectroscopy of the Andreev reflection in point contact Ag-Dy_{0.8}Y_{0.2}Rh_4B_4 the value and temperature and field dependences of superconducting gap parameter∆(T, H) in Dy_{0.8}Y_{0.2}Rh_4B_4 were determined. The value of the ratio 2∆(0)/kT_C is about 4. Some unusual features of∆(T, H) dependences were observed, which give the evidence that the Dy_{1-x}Y_xRh_4B_4 is a candidate for spin-triplet Cooper pairing of charges with the parallel spins.
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