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The temporal evolution of the pulsed positive streamer discharge in water is investigated by high-speed photography. Four successive one-shot photographs were acquired from the same discharge pulse. Two modes of streamer propagation, called the first mode and the second mode, were confirmed from the time-resolved images. The first-mode streamer appears as an expanding luminous plasma ball, and no filament can be recognized at this stage. The standing time and the maximum radius of the luminous plasma ball are 40-60 ns and 600-800 μm, respectively. Then, the streamer transits to the second mode, in which many luminous filaments grow up from the plasma ball. At the beginning of the second mode, all the filaments propagate isotropically from the plasma ball and have an equal propagation velocity. Only some of the filaments originated from the plasma ball can propagate furthermore, and most of them spontaneously disappear in about 40 ns. After it reaches the stopping length, the streamer stops propagating but remains luminous. As the discharge voltage drops down, the brightness of the streamer decreases, and the light shrinks successively from the streamer head to the tip of the point anode. Our measured propagation velocity for the first mode is about 25 km/s. The propagation velocity increases about two times as the streamer transits from the first mode to the second mode and then reduces approximately to the same value for the first mode. The water conductivity has no significant influence on the propagation velocity within the range studied.