Context. The Galactic bulge has a bimodal metallicity distribution function: different kinematic, spatial, and, potentially, age distributions characterize the metal-poor and metal-rich components. Despite this observed dichotomy, which argues for different formation channels for those stars, the distribution of bulge stars in the α-abundance versus metallicity plane has been found so far to be a rather smooth single sequence. Aims. We use data from the fourteenth data release of the APOGEE spectroscopic survey (DR14) to investigate the distribution in the Mg abundance (as tracer of the α-elements)-versus-metallicity plane of a sample of stars selected to be in the inner region of the bulge. Methods. A clean sample has been selected from the DR14 using a set of data- and pipeline-flags to ensure the quality of their fundamental parameters and elemental abundances. An additional selection made use of computed spectro-photometric distances to select a sample of likely bulge stars as those with R_GC ≤ 3.5 kpc. We adopt magnesium abundance as an α-abundance proxy for our clean sample as it has been proven to be the most accurate α-element as determined by ASPCAP, the pipeline for data products from APOGEE spectra. Results. From the distribution of our bulge sample in the [Mg/Fe]-versus-[Fe/H] plane, we found that the sequence is bimodal. This bimodality is given by the presence of a low-Mg sequence of stars parallel to the main high-Mg sequence over a range of ∼0.5 dex around solar metallicity. The two sequences merge above [Fe/H] ∼ 0.15 dex into a single sequence whose dispersion in [Mg/Fe] is larger than either of the two sequences visible at lower metallicity. This result is confirmed when we consider stars in our sample that are inside the bulge region according to trustworthy Gaia DR2 distances.