The invention relates to a process for separating a multi-component feed mixture in a distillation system comprising a first distillation column having a first fired reboiler, and at least a second distillation column having a second heat-exchange reboiler, comprising the steps of a) introducing the feed mixture to the first column, and separating into at least a first top and a first bottom product; b) taking part of the first bottom product for providing heat to the second reboiler as a utility stream; and c) feeding part of said utility stream after heat-exchange as main feed to the second column for further separation. This process allows significant energy savings, by reduction of the amount of external heat required for the fired reboiler and omission of a conventionally used heat-exhanger. The invention also relates to such distillation system suitable for separating a multi-component mixture with the process of the invention.