We present a new ultrathin metamaterial that acts as a frequency-selective absorber of terahertz radiation. The absorber is a square array of pairs of omega-shaped micro-resonators made of high-ohmic-loss metal. The metamaterial provides significant suppression of transmitted and reflected radiation in a bidirectional regime (that is, for both forward and backward propagating radiation). The absorber is efficient in a wide range of angles of incidence. The absence of a ground plane makes the absorber unique in comparison with numerous analogs with a ground plane that operate in a unidirectional regime. The novel metamaterial potentially enables controllable transmission of terahertz radiation in imaging systems. Analytical calculations as well as finite-element electromagnetic modeling are presented for an exemplary case with peak absorption at ∼3 THz.