There is disclosed an electronic instrument intended to be worn on a user's wrist, such as a wristwatch (1), including a case (2) and a wristband (2a) secured to the case. The case encloses an electronic module (6), a display device (5) and an electric power source (10) powering the electronic module and the display device. This instrument further includes an antenna (20) arranged in an off-centre position with respect to the centre () of the instrument. The instrument is configured to be worn on the wrist in a first, so-called normal position, and in a second, so-called opposite position, rotated through 180 with respect to the first position about an axis () substantially perpendicular to the general plane () of the electronic instrument. The instrument further includes control means for switching the display device into a first so-called normal display mode, when the instrument is worn in the first position, and into a second so-called reverse display mode, when the instrument is worn in the second position, the data displayed by the display device being shifted through 180 from one display mode to the other.