The problem of constructing first-order saturated designs that are optimal in some sense has received a great deal of attention in the literature. In experimental situations where n two-level factors are involved and n observations are taken, then the D-optimal first-order saturated design is an n × n ± 1 matrix with the maximum determinant. In this paper almost D-optimal first-order saturated designs of order n ≡ 1 mod 4 are constructed using Hadamard matrices with maximum excess. The D-efficiency of these designs is studied and some numerical examples are given.