This paper modified an existing 3–point block method for solving stiff initial value problems.  The modification leads to the derivation of another 3 – point block method which is suitable for solving stiff initial value problems.  The method approximates three solutions values per step and its order is 5. Different sets of formula can be generated from it by varying a parameter ρ ϵ (-1, 1) in the formula. It has been shown that the method is both Zero stable and A–Stable. Some linear and nonlinear stiff problems are solved and the result shows that the method outperformed an existing method and competes with others in terms of accuracy

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