This paper examines a search-matching model in which match specific output follows a geometric Brownian motion. As opposed to Poisson Processes, Brownian motions generate a negative correlation between job output and the likelihood of separation. Introducing geometric Brownian motion improves the fit of the standard model with respect to the observed patterns of worker turnover and wage dispersion, without taking from its relevance at the macro level. Firstly, the proposed set-up does not require learning about match quality in order to yield a hump-shaped hazard rate of job separation. Secondly, the aggregate wage distribution is unimodal and its right tail belongs to the Pareto family, so it satisfies the "heavy-tail" property that is commonly observed in the data.