An algorithm based on a new approach for solving the F2|overlap|Cmax scheduling problem is discussed. In preparation for the discussion, we introduce two special schedule types, a ‘quasi 0 shaped schedule’ and an ‘absolute 0 shaped schedule’. A demonstrative proof for Johnson's algorithm for the F2‖Cmax problem is also discussed. We give theorems and their proofs to show that the new algorithm gives solutions for problems F2‖Cmax, F2|idle|Cmax and F2|overlap, idle|Cmax as well.