Black hole binary (BHB) systems comprise a stellar-mass black hole and a closely orbiting companion star. Matter is transferred from the companion to the black hole, forming an accretion disk, corona and jet structures. The resulting release of gravitational energy leads to the emission of X-rays(1). The radiation is affected by special/general relativistic effects, and can serve as a probe for the properties of the black hole and surrounding environment, if the accretion geometry is properly identified. Two competing models describe the disk-corona geometry for the hard spectral state of BHBs, based on spectral and timing measurements(2,3). Measuring the polarization of hard X-rays reflected from the disk allows the geometry to be determined. The extent of the corona differs between the two models, affecting the strength of the relativistic effects (such as enhancement of the polarization fraction and rotation of the polarization angle). Here, we report observational results on the linear polarization of hard X-ray emission (19-181 keV) from a BHB, Cygnus X-1(4), in the hard state. The low polarization fraction, <8.6% (upper limit at a 90% confidence level), and the alignment of the polarization angle with the jet axis show that the dominant emission is not influenced by strong gravity. When considered together with existing spectral and timing data, our result reveals that the accretion corona is either an extended structure, or is located far from the black hole in the hard state of Cygnus X-1.