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We demonstrate that abundant quantities of short-lived beta unstable ions can be trapped in a novel transparent Paul trap and that their decay products can directly be detected in coincidence. Low energy 6He+ (807 ms half-life) ions were extracted from the SPIRAL source at GANIL, then decelerated, cooled, and bunched by means of the buffer gas cooling technique. More than 10(8) ions have been stored over a measuring period of six days, and about 10(5) decay coincidences between the beta particles and the 6Li++ recoiling ions have been recorded. The technique can be extended to other short-lived species, opening new possibilities for trap assisted decay experiments.