For uncertain linear system subjected to uniformly bounded unknown inputs it is presented a novel finite-time unknown input first-order sliding-mode observer. The strategy involves the design of a pair of quadratically stable first-order sliding-mode observers, aimed to guarantee the robustness to non-smooth unknown inputs and the finite-time convergence to zero of the output estimation errors. Then, the exact estimation of the unmeasured states is achieved in a fixed-time since the sliding motion is established through the design of an auxiliary output consisting of a delayed linear-combination of the estimations provided by the above-mentioned pair of observers. To confirm the effectiveness of the proposed scheme, along with a sketch of the proof of its convergence characteristics, a detailed numerical comparison analysis with the existing first-order sliding-mode competitor observers is illustrated.