Exotic polarization domain configurations in BiFeO3 nanoislands have recently been achieved, promising for exploring next-generation nanoelectronics. Here, different from the earlier reported BiFeO3 nanoislands with a very thin cross-shaped domain wall on LaAlO3 substrates, we observed the cross-shaped domains with a downward polarization separating quad-domains with an upward polarization, which is confirmed by spherical aberration corrected scanning transmission electron microscopy and piezoresponse force microscopy. Interestingly, the cross- and quad-domains show diode-like transport behaviors but with different rectification directions owing to their different polarization orientations. Specifically, an intriguing two-step ferroelectric polarization switching can be realized, which locally results in a tri-state nonvolatile memory. These results broaden the understanding of the interesting polarization configurations in BiFeO3 nanoislands and highlight their potential as high-density information storage.