Visual processing involves hierarchical stages in which local features are initially analyzed and subsequently grouped into objects and surfaces. In the domain of motion perception, transparent motion has been used as a powerful tool to investigate the mechanisms underlying the grouping of local features. Here, we report a novel way of creating motion transparency from oscillating dots (MTOD). In this stimulus, individual dots move back and forth over a small distance. When the dots are oscillating in synchrony, global surfaces are also perceived as moving back and forth. However, when the oscillation desynchronizes, the percept turns into two moving surfaces that are sliding over each other continuously (streaming motion). The percept of MTOD is similar to conventional transparent motion, where individual dots move only in one direction. Also, when streaming motion is perceived, the detection of oscillation is impaired. This blindness to the oscillation becomes stronger, as the signal strength for the streaming motion is increased. These findings suggest that when global visual representations are constructed, weak and inconsistent local signals are discarded.