The 115In NQR spectra in layered InSe single crystals for four spin transitions, the average values of which only approximately satisfied the ratio v1:v2:v3:v4 =1:2:3:4 were studied. It was found that for higher transitions a deviation is observed. In particular, it is shown that additional lines are observed in the multiplet groups for higher-order transitions, which, in our opinion, is associated with the presence of a hexadecapole interaction with the gradient of the crystal electric field.