In this work, a block of diagonally implicit backward differentiationmethodwith two off-step points for solving first orderstiff initial value problem of ordinary differential equation wasderived. In the proposed block method two approximate solution values of 𝑦𝑛+1and 𝑦𝑛+2with two off-step points 𝑦𝑛+12and 𝑦𝑛+32are computed concurrently for each iteration. The properties of the newly proposed method were found to be an A-stable, Zero stable and capable for solving first order Stiff IVPs. To validate the performance of the proposed method, some first order stiff IVPs are solved and the result obtained was compared with other existing numerical schemes. From the tabulated results and the graphs plotted, the proposed methodhas shown advantages of accuracy in the scale error over the three methods and an advantage of executional time over two of the existing methods considered.
