Exotic electronic states resulting from entangled spin and orbital degrees of freedom are hallmarks of strongly correlated f-electron systems. A spectacular example is the so-called hidden-order (HO) phase transition in the heavy-electron metal URu2Si2, which is characterized by the huge amount of entropy lost at THO=17.5K (refs , ). However, no evidence of magnetic/structural phase transition has been found below THO so far. The origin of the HO phase transition has been a long-standing mystery in condensed-matter physics. Here, on the basis of a first-principles theoretical approach, we examine the complete set of multipole correlations allowed in this material. The results uncover that the HO parameter is a rank-5 multipole (dotriacontapole) order with nematic E- symmetry, which exhibits staggered pseudospin moments along the  direction. This naturally provides comprehensive explanations of all key features in the HO phase including anisotropic magnetic excitations, the nearly degenerate antiferromagnetic-ordered state and spontaneous rotational-symmetry breaking.