Fission of doubly charged sodium clusters is studied using the open-shell two-center deformed jellium model approximationand ab initio molecular dynamic approach accounting for all electrons in the system. Results of calculations of fission reactions Na₁₀²⁺ → Na₇⁺ + Na₃⁺ and Na₁₈²⁺ → 2 Na₉⁺ are presented. Dependence of the fission barriers on isomer structure of the parent cluster is analyzed. 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 on the daughter fragments begins and/or forming a "neck" between the separating fragments.