The linear phase is a major characteristic of digital differentiators in many signal processing applications.This study presents a sequential partial optimization method for designing a fullband infinite impulse response digital differentiator with a near linear phase.To achieve a near linear phase,the group delay is treated as an optimization variable,and the maximum phase error is minimized within a constrained domain.During each iteration of the algorithm,in addition to the whole numerator and group delay,only one second-order denominator factor is optimized.The necessary and sufficient stability triangles are applied to insure the stability of the differentiators,and the Gauss-Newton strategy is used to handle the nonconvexity of the design problems.Design examples show that the proposed method outperforms several state-of-the-art methods in terms of the maximum phase deviation from the desired linear phase.