Kristjánite, KNa₂H(SO₄)₂, is a new mineral found in a high-temperature fumarole on Fimmvör∂uháls, Iceland. It is monoclinic, P2₁/n, a, b, c (Å) = 6.9625(1), 9.9953(1), 11.0928(2), β = 105.637(2)°, V = 743.40(2) Å₃. Kristjánite forms colourless transparent crystals up to about 100 μm in size in compact aggregates with metathénardite, belomarinaite, aphthitalite, ivsite and an unknown mineral with tentative composition K₂NaH(SO₄)₂, or grows in white globules of smaller grains on their surface. The eight strongest maxima in a Powder X-Ray Diffraction diagram are [d(Å)_Intensity] 4.37₆, 3.65₃, 3.48₈, 3.36₁₀, 3.18₈, 2.83₄, 2.73₄and 2.405₂. The mineral represents a novel crystal structure type. In it, K is coordinated by eight O atoms, and two symmetrically independent Na atoms by seven O atoms. Two symmetrically independent S atoms are in tetrahedral coordination by O atoms. A close to linear, very short hydrogen bond (2.44 Å), connects the two to a SO₄-H-SO₄dimer. K and Na coordination polyhedra share vertices, edges and even faces forming with sulphate tetrahedra a tight structure with narrow [100] channels lined on two opposite sides by hydrogen bonds.