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Orthogonal strip detectors are single-carrier devices that allow reduction of the amount of read-out channels while obtaining a good spatial resolution. They are especially interesting for low count rate imaging applications like gamma-ray medical imaging. Nevertheless, applying a bias voltage between and strips is necessary in order to localize correctly the interactions. Unfortunately, this bias voltage induces a leakage current, thus generating an unwanted shot noise. We propose in this paper a new setup using capacitive contacts, which suppresses leakage currents between collecting and non-collecting strips. In this paper, we first briefly present the state-of-the-art relative to coplanar grid and strip detectors, their advantages and their drawbacks. In a second part, we will focus on the theoretical background of the capacitive contact. In a third part, a simulation study of the electrode geometry is reported. Thanks to the spectral approach, we have computed the 3D applied and weighting electric fields, bulk resistances and capacitances for various geometries of the design. Afterwards, we have used these data to simulate pulse waveforms and study the associated electronics. Finally the fabrication of the devices is presented and our first experimental results are reported. As a conclusion, we will discuss the interests and the limitations of this kind of device.