Most superconducting materials are well understood and conventional-that is, the pairs of electrons that cause the superconductivity by their condensation have the highest possible symmetry. Famous exceptions are the enigmatic high-temperature (high-Tc) cuprate superconductors1. Nodes in their superconducting gap are the fingerprint of their unconventional character and imply superconducting pairing of d-wave symmetry. Here, by using angle-resolved photoemission spectroscopy, we observe that the Weyl semimetal PtBi2 harbours nodes in its superconducting gap, implying unconventional i-wave pairing symmetry. At temperatures below 10 K, the superconductivity in PtBi2 gaps out its topological surface states, the Fermi arcs, whereas its bulk states remain normal2. The nodes in the superconducting gap that we observe are located exactly at the centre of the Fermi arcs and imply the presence of topologically protected Majorana cones around this locus in momentum space. From this, we infer theoretically that robust zero-energy Majorana flat bands emerge at surface step edges. This establishes PtBi2 surfaces not only as unconventional, topological i-wave superconductors but also as a promising material platform in the ongoing effort to generate and manipulate Majorana bound states.