A new Fourier transform ion cyclotron resonance (FTICR) cell based on completely new principles of formation of the effective electric potential distribution in Penning type traps, Boldin and Nikolaev (Proceedings of the 58th ASMS Conference, 2010), Boldin and Nikolaev (Rapid Commun Mass Spectrom 25:122-126, 2011) is constructed and tested experimentally. Its operation is based on the concept of electric potential space-averaging via charged particle cyclotron motion. Such an averaging process permits an effective electric force distribution in the entire volume of a cylindrical Penning trap to be equal to its distribution in the field created by hyperbolic electrodes in an ideal Penning trap. The excitation and detection electrodes of this new cell are shaped for generating a quadratic dependence on axial coordinates of an averaged (along cyclotron motion orbit) electric potential at any radius of the cyclotron motion. These electrodes together with the trapping segments form a cylindrical surface like in a conventional cylindrical cell. In excitation mode this cell being elongated behaves almost like an open cylindrical cell of the same length. It is more effective in ion motion harmonization at larger cyclotron radii than a Gabrielse et al.-type (Int J Mass Spectrom Ion Processes 88:319-332, 1989) cylindrical cell with four compensation sections. A mass resolving power of more than twenty millions of reserpine (m/z 609) and more than one million of highly charged BSA molecular ions (m/z 1357) has been obtained in a 7T magnetic field.