Method for enhancing a recording signal in a binaural hearing system with at least a first hearing aid, the first hearing aid comprising a first directional microphone having an adjustable first directional characteristic with a preferred direction, wherein the first directional microphone converts sound into a first signal which is included in the recording signal, wherein the binaural hearing system comprises a second hearing aid comprising a second directional microphone, wherein the second directional microphone converts sound into a second signal which is included in the recording signal, wherein a speech activity of a user of the hearing system is monitored, wherein, when a speech activity of the user is detected, the preferred direction of the first directional characteristic is adjusted relative to a frontal direction of the user in such a way that the sound sensitivity of the first directional microphone is attenuated in the frontal direction, wherein the preferred direction of the first directional microphone is adjusted at an angle between 5° and 20° with respect to the frontal direction of the user, wherein, when the speech activity of the user is detected, the preferred direction of the second directional characteristic is adjusted relative to a frontal direction of the user in such a way that the second directional characteristic undergoes attenuation in the frontal direction, wherein the preferred direction of the second directional characteristic is adjusted at an angle between 5° and 20° relative to the frontal direction of the user, and wherein, when the speech activity of the user is detected, the preferred directions (12, 18) of the first directional characteristic and of the second directional characteristic are adjusted with respect to the frontal direction of the user in such a way that the preferred directions (12, 18) of the first directional characteristic and of the second directional characteristic are crossing each other. wherein the first directional microphone converts sound into a first signal which is included in the recording signal, wherein the binaural hearing system comprises a second hearing aid comprising a second directional microphone, wherein the second directional microphone converts sound into a second signal which is included in the recording signal, wherein a speech activity of a user of the hearing system is monitored, wherein, when a speech activity of the user is detected, the preferred direction of the first directional characteristic is adjusted relative to a frontal direction of the user in such a way that the sound sensitivity of the first directional microphone is attenuated in the frontal direction, wherein the preferred direction of the first directional microphone is adjusted at an angle between 5° and 20° with respect to the frontal direction of the user, wherein, when the speech activity of the user is detected, the preferred direction of the second directional characteristic is adjusted relative to a frontal direction of the user in such a way that the second directional characteristic undergoes attenuation in the frontal direction, wherein the preferred direction of the second directional characteristic is adjusted at an angle between 5° and 20° relative to the frontal direction of the user, and wherein, when the speech activity of the user is detected, the preferred directions (12, 18) of the first directional characteristic and of the second directional characteristic are adjusted with respect to the frontal direction of the user in such a way that the preferred directions (12, 18) of the first directional characteristic and of the second directional characteristic are crossing each other.