The present invention relates to estimating the attitude angles of an aircraft (1). The estimated attitude angles are generated by a device (9) that performs algorithmic integration on inertial measurements indicative of an angular velocity and of a linear acceleration. Horizontal components (34-39) of desired corrections are obtained by a linear combination of two horizontal components (32-33), with cross coefficients between said horizontal axes being continuous variable over time and dependent on the estimated rate of turn. As a result, the estimated attitude angles are stable, and the biases of the gyros continue to be estimated, including during stages during which the aircraft (1) is turning.