We introduce a new technique to search for gravitational wave events from compact binary mergers that produce a clear signal only in a single gravitational wave detector, and marginal signals in other detectors. Such a situation can arise when the detectors in a network have different sensitivities, or when sources have unfavorable sky locations or orientations. We start with a short list of loud single-detector triggers from regions of parameter space that are empirically unaffected by glitches (after applying signal-quality vetoes). For each of these triggers, we compute evidence for astrophysical origin from the rest of the detector network by coherently combining the likelihoods from all detectors and marginalizing over extrinsic geometric parameters. We report the discovery of two new binary black hole (BBH) mergers in the second observing run of Advanced LIGO and Virgo (O2), in addition to the ones that were reported in Abbott et al. (2018) and Venumadhav et al. (2019). We estimate that the two events have false alarm rates of one in 19 years (60 O2) and one in 11 years (36 O2). One of the events, GW170817A, has primary and secondary masses $m_1^{rm src} = 56_{-10}^{+16} , M_odot$ and $m_2^{rm src} = 40_{-11}^{+10} , M_odot$ in the source frame. The existence of GW170817A should be very informative about the theoretically predicted upper mass gap for stellar mass black holes. Its effective spin parameter is measured to be $chi_{rm eff} = 0.5 pm 0.2$, which is consistent with the tendency of the heavier detected BBH systems to have large and positive effective spin parameters. The other event, GWC170402, will be discussed thoroughly in future work.
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