  Double-decker filaments and their eruptions have been widely observed in
recent years, but their physical formation mechanism is still unclear. Using
high spatiotemporal resolution, multi-wavelength observations taken by the New
Vacuum Solar Telescope and the Solar Dynamics Observatory, we show the
formation of a double-decker pair of flux rope system by two successive
tether-cutting eruptions in a bipolar active region. Due to the combined effect
of photospheric shearing and convergence motions around the active region's
polarity inversion line (PIL), the arms of two overlapping inverse-S-shaped
short filaments reconnected at their intersection, which created a simultaneous
upward-moving magnetic flux rope (MFR) and a downward-moving post-flare-loop
(PFL) system striding the PIL. Meanwhile, four bright flare ribbons appeared at
the footpoints of the newly formed MFR and the PFL. As the MFR rose, two
elongated flare ribbons connected by a relatively larger PFL appeared on either
side of the PIL. After a few minutes, another MFR formed in the same way at the
same location and then erupted in the same direction as the first one. Detailed
observational results suggest that the eruption of the first MFR might
experienced a short pause before its successful eruption, while the second MFR
was a failed eruption. This implies that the two newly formed MFRs might reach
a new equilibrium at relatively higher heights for a while, which can be
regarded as a transient double-decker flux rope system. The observations can
well be explained by the tether-cutting model, and we propose that two
successive confined tether-cutting eruptions can naturally produce a
double-decker flux rope system, especially when the background coronal magnetic
field has a saddle-like distribution of magnetic decay index profile in height.
