This article proposes a methodology for estimating the attitude of a rigid body from vector measurements only, i.e. without gyrometers. Classically, two vector measurements are enough to determine the attitude of a rigid body, through an algebraic calculation which is sometimes considered as computationally costly or tedious to implement. Instead, simple observers are often implemented such as the attitude complementary filter, using the feedback of a (possibly biased) gyrometer. What we show in this article is that the angular velocity can be simply estimated with the vector measurements, thus making the gyro redundant. We propose an adaptation of the complementary filter that is simple to implement and gyroless. A proof of convergence is given, and simulation and experimental results are provided.