This paper develops a matching model of the labor market under wage rigidity when hiring decisions are irreversible. There are two types of workers, the skilled and the unskilled. The model is used to analyze whether technological advances may have increased unemployment. It is shown that it is likely to be so if they are associated with an increase in the productivity and/or the supply of skilled workers relative to unskilled workers. These effects are stronger when hiring decisions are more irreversible.