Tam180 is the rarest naturally occurring quasistable isotope and the longest lived metastable state which is known. Its possible decay via the β- or the electron capture channel has never been observed. This article presents a search for the decay of Tam180 with an ultralow background Sandwich HPGe γ spectrometry setup in the HADES underground laboratory. No signal is observed and improved lower partial half-life limits are set with a Bayesian analysis to 5.8 ×1016yr for the β- channel and 2.0 ×1017yr for the electron capture channel (90 % credibility). The total half-life of Tam180 is longer than 4.5 ×1016yr . This is more than a factor of two improvement compared to previous searches.