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Abstract We have systematically investigated the decuplet (T) to octet (B) baryon ($$T\rightarrow B\gamma $$ T→Bγ ) transition magnetic moments to the next-to-next-to-leading order and electric quadruple moments to the next-to-leading order in the framework of the heavy baryon chiral perturbation theory. Our calculation includes the contributions from both the intermediate decuplet and octet baryon states in the loops. Throughout our calculation, we have adopted the small-scale scheme and have not considered the 1/M recoiling corrections directly. We count the octet and decuplet baryon mass splitting $$\delta $$ δ , the small momenta p, and the pion mass $$m_{\phi }$$ mϕ as the same order small-scale parameter, which was denoted as $$\epsilon $$ ϵ . Our results for the transition magnetic moments show reasonably good convergence of the chiral expansion. The analytical expressions may be useful to the chiral extrapolation of the lattice simulations of the decuplet electromagnetic properties.