Results of molecular dynamics simulations of fission reactionsNa₁₀²⁺→ Na₇⁺+ Na₃⁺ and Na₁₈²⁺→ 2Na₉⁺ are presented. The dependence of the fission barriers on the isomer structure of the parent cluster is analysed. It is demonstrated that the energy necessary for removing homothetic groups of atoms from the parent cluster is largely independent of the isomer form of the parent cluster. The importance of rearrangement of the cluster structure during the fission process is elucidated. This rearrangement may include transition to another isomer state of the parent cluster before actual separation of the daughter fragments begins and/or forming a 'neck' between the separating fragments.