This paper proposes a new adaptation-mode control (AMC) for a robust adaptive microphone array with an adaptive blocking matrix (RAMA-ABM). The proposed AMC is based on cross correlations of two microphone signals and uses a state machine for controlling the adaptation to avoid target-signal cancellation. Evaluation with sound data obtained in different acoustic environments demonstrates that the noise reduction by the proposed AMC is 3 dB better than that by the AMC based on the SNR estimate. Subjective listening tests show that the quality of the output signal by the proposed AMC is comparable to or even better than those by the conventional AMCs.