The effect of three-spin interaction k on thermal entanglement between alternate qubits is studied using pairwise concurrence C and energy-level diagram. It is found that k breaks the symmetry about the effect of magnetic field h on C. It shifts a dip structure and gradually effaces a boot structure when $$\left| k \right| <\left| J \right| $$ k < J (J is spin exchange coupling). A peak with C maintains 1 appears and expands, elbowing the dip backwards when $$\left| k \right| >\left| J \right| $$ k > J . A sudden change in the concurrence occurs around $$\left| k \right| =\left| J \right| $$ k = J , $$h=-k$$ h = - k . Similar conclusions about nearest-neighbor qubits are directly given.