We take a fresh look at the SU(3) systematization of all known baryons with mass less than 2000 MeV. We describe well-known and new theoretical tools used in grouping elementary particles into unitary multiplets and present the emerging picture of the unitary multiplets and their mixing. The issue of multiplet mixing is discussed in detail with an emphasis on the mixing with the antidecuplet. While SU(3) does not strongly require that the antidecuplet mixes with any established octet or decuplet, it is still possible to mix the antidecuplet with a JP=1/2+ octet. However, the mixing parameters cannot be reliably determined this way. Instead, one should consider decays of the antidecuplet members.