In this paper, we propose a method called the iterated estimation of kernel and error (KE estimation) to find the maximum-likelihood (ML) estimate of the error-diffusion (ED) kernel for halftones. The KE estimation consists mainly of iterated boundconstrained least squares (BLS). The KE-estimated kernel avoids the difficulty of regulating the control parameter in the previous least-mean-square (LMS) method. Most importantly, our method also guarantees the two characteristics of ED kernel: every kernel coefficient falls in the range [0,1] and the total of all coefficients must be one. The experimental results show that using the KE estimation to estimate kernel for the halftones generated from an ED process is very effective. The estimate progressively increases its accuracy as the number of iterations increases.