Small-scale internetwork magnetic fields are important ingredients of the quiet Sun. In this paper we analyze how they appear and disappear on the solar surface. Using high resolution Hinode magnetograms, we follow the evolution of individual magnetic elements in the interior of two supergranular cells at the disk center. From up to 38 hr of continuous measurements, we show that magnetic flux appears in internetwork regions at a rate of $120pm3$ Mx cm$^{-2}$ day$^{-1}$ ($3.7 pm 0.4 times 10^{24}$ Mx day$^{-1}$ over the entire solar surface). Flux disappears from the internetwork at a rate of $125 pm 6$ Mx cm$^{-2}$ day$^{-1}$ ($3.9pm 0.5 times 10^{24}$ Mx day$^{-1}$) through fading of magnetic elements, cancellation between opposite-polarity features, and interactions with network patches, which converts internetwork elements into network features. Most of the flux is lost through fading and interactions with the network, at nearly the same rate of about 50 Mx cm$^{-2}$ day$^{-1}$. Our results demonstrate that the sources and sinks of internetwork magnetic flux are well balanced. Using the instantaneous flux appearance and disappearance rates, we successfully reproduce the time evolution of the total unsigned flux in the two supergranular cells.
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