Abstract We present new [Ne ii] (12.8 μm) IRTF/TEXES observations of the Galactic Center H ii regions H1 and H2, which are at a projected distance of ∼11 pc from the centre of the Galaxy. The new observations allow us to map the radial velocity distributions of ionized gas. The high spectroscopic resolution (∼4 km s−1) helps us to disentangle different velocity components and enables us to resolve previous ambiguity regarding the nature of these sources. The spatial distributions of the intensity and radial velocity of the [Ne ii] line are mapped. In H1, the intensity distributions of the Paschen-α (1.87 μm) and [Ne ii] lines are significantly different, which suggests a strong variation of extinction across the H ii region of AK ∼ 0.56. The radial velocity distributions across these H ii regions are consistent with the predictions of a bow-shock model for H1 and the pressure-driven model for H2. Furthermore, we find a concentration of bright stars in H2. These stars have similar H − Ks colours and can be explained as part of a 2-Myr-old stellar cluster. H2 also falls on the orbit of the molecular clouds, suggested to be around Sgr A*. Our new results confirm what we had previously suggested: The O supergiant P114 in H1 is a runaway star, moving towards us through the −30 to 0 km s−1 molecular cloud, whereas the O If star P35 in H2 formed in situ, and may mark the position of a so-far unknown small star cluster formed within the central 30 pc of the Galaxy.