The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC), omitting thedifference between the two components, has been studied using an analytical method. The energy eigenstates andeigenvalues for L＝0,1,2,3 are given. We illustrate that there are different eigenstate behaviours between the even Land odd L cases for the two-component BEC in two dimensions. Except for symmetric states, there are antisymmetricstates for the permutation of the two components, which cannot reduce to those in a single condensate case when thevalue of L is odd.