It is known that high symmetric polyatomic molecules and clusters with an orbital degenerated ground state are distorted and their symmetry is lowered due to the Jahn-Teller effect [1]. By analogy with Jahn-Teller instability, Kahn [2] suggested that the spin populations of an equilateral trimer with generated ground state and nonzero spin moment are unstable with respect to a weak structural distortion. He analyzed the competing spin interactions in an equilateral triangle of half-integer spin in the simple case S1 = S2 = S3 = 1 2 . The antiferromagnetic interactions in such a triangle lead to an orbital degenerated frustrated ground state. In this case, the two Kramers doublets that represent two components of the degenerate ground state (1 2⊗1 2⊗1 2 = 2(1 2)⊕3 2) are 1/ 2,0 and 1/ 2,1 (0 and 1 are the values of the intermediary spin). Assuming that Zeeman factor g is equal to 2.00, the spin populations (in Nβ units) at the corners of the triangle were found as: 0, 1, 0 for S’=0 and 2/3, -1/3, 2/3 for S’=1, respectively. The above indicated instability of spin populations with respect to a weak perturbation transforming the equilateral triangle (with perfect C3 symmetry) into an isosceles one take place [2] for the ground state Kramers doublet. However, this reasoning is incorrect [3] because any distortion-induced spin polarization resulting from two ground state spin wave functions (denoted as Φ 1 and Φ 3 in [3]) will be canceled out by the opposite spin polarization resulting from Φ 2 and Φ 4 ground state spin wave functions (see ref. 3). We note that only pure spins without orbital contribution were taken into account in ref. 2, so that the splitting of the 2E term in C3 symmetry due to spin-orbit coupling was ignored. In this work we evaluate the direct and opposite distortion-induced spin polarizations in case of high values of the spins S1 = S2 = S3 = 5/2. It is found that the structure of the ground state spin wave functions related to the two Kramers doublets at high values of spins causes the same behavior as the spin system concerning total compensation of the distortion-induced spin polarization, as for the simple case S1 = S2 = S3 = 1 2 . In view of the fact that at high values of spins the spin wave functions of trimer cluster are unwieldy they are presented only for two ground Kramers doublets in the case of S1 = S2 = S3 = 1 2 .It is shown that the spin moments given by 1 Ψ and Ψ3 are the same in magnitude as, but opposite in sign from, those given by Ψ2 and Ψ4 , respectively. Here 1 Ψ and 3 Ψ are the components of the ground state Kramers doublet arising from D2 (1,2)⊗ D5 2 (3) direct product of representations (1,2 and 3 in brackets denote spin Sμ sites) while 2 Ψ and Ψ4 are the components of the second ground state Kramers doublet arising from D3(1,2)⊗ D5 2 (3). Thus, any distortion-induced spin polarization resulting from Ψ1 and Ψ3 will be canceled out by the opposite spin polarization resulting from Ψ2 and Ψ4 . This result is in excellent agreement with obtained early data [3] for symmetrical spin trimers with S1 = S2 = S3 = 1 2 . Moreover, our calculations of the resulting distortion-induced spin polarization in the ground state of symmetrical spin trimers show that such spin polarization is forbidden for Si = 3 2 and Si = 7 2 (i=1,2,3) as well as for Si = 1 2 and Si = 5 2 . Such behavior of the symmetrical spin trimer clusters at any half-integer values of Si (i=1,2,3) is caused by the same symmetry properties of the spin wave functions related to both ground state Kramers doublets.