The table of 24 stars in one of the two extant manuscripts of the Mumtaḥan zīj is the earliest non-Ptolemaic star table in medieval Middle Eastern astronomy. Dated to 829 AD, it is a fruit of the two The table of 24 stars in one of the two extant manuscripts of the Mumtaḥan zīj is the earliest non-Ptolemaic star table in medieval Middle Eastern astronomy. Dated to 829 AD, it is a fruit of the two systematic observational programs carried out by a group of astronomers in Baghdad and Damascus in the early ninth century. In this study, the accuracy of this table is examined, showing the existence of an obvious systematic negative error in the longitude values. The manuscripts also contain another table of 18 stars, all of which also appear in the first table, in which the longitudes are updated for 1011 AD. This table is further updated for 1231 AD in the Īlkhānī zīj, the official product of the observational programs in the Maragha observatory, northwestern Iran, in the 1260s, where it is ascribed to Ibn al-A‘lam (d. 985 AD). In this paper, some verifiable and convincing proofs are provided for the hypothesis that the second Mumtaḥan star table is quite probably a refinement of the first table made by Ibn al-A‘lam on the basis of a few stellar observations by himself dated to about 976 AD. Firm evidence for one of these observations, namely of Regulus (α Leo), is provided by his younger contemporary Ibn Yūnus (d. 1009 AD).