A new two-step Extended Second Derivative Hybrid Block Backward Differentiation Formula (ESDHBBDF) for the solution of Differential-algebraic Equations (DAEs) of index-1, 2, and 3 systems is presented. The derived methods which were coupled and implemented as a set of block formulae was implemented in a block by block fashion. Numerical results obtained when tested on some standard DAEs of index- 1, 2, and 3 with wider range revealed that the method was efficient and very accurate, and particularly suitable for DAEs.