HTTP adaptive streaming (HAS) can achieve low latency for live streaming with the Common Media Application Format. However, the legacy mechanisms inaccurately measure the available bandwidth because the download time is affected by not only the network but also idle times between chunks at the live encoder side. These wrong measurements may condemn users to a low quality-of-experience (QoE). This letter presents a HAS client with a novel bandwidth measurement heuristic. Our experiments show that it provides a better QoE with fewer video freezes and higher video quality while achieving a live latency down to one second in bandwidth-limited networks.