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We propose a new array covariance matrix analysis method, named 'maximum covariance direction method' (MCD method), to detect and locate unconventional seismic sources of weak signals without clear onsets. The MCD method builds a normalized-covariance matrix of time-shifted seismic waveforms recorded in a seismic array and determines the existence of source based on the consistency of the maximum covariance direction with the theoretical prediction. Synthetic tests demonstrate effectiveness of the MCD method in detecting one and multiple isolated sources with low signal-to-noise ratios. As a data application, we study 1-hr long-period tremors (LPTs) around Aso Volcano of Japan in 2014 November 24. A total of 26 LPTs are detected near the Naka-dake first crater of Aso Volcano, with the uncertainties of source location of about 7 km. Using the recorded background noise at the seismic stations, we show that the MCD method can detect LPTs even when the LPT signals are buried in the background noise and become indiscernible in the seismic data. Unlike traditional methods that employ the coherent features of seismic signals for source detection, the MCD method places emphases on both the coherence of seismic signals and consistency of the direction of the coherent signals from a potential source location. The synthetic tests and data application indicate that the MCD method provides a good alternative to other traditional methods for detecting and locating unconventional seismic sources, with a major improvement of avoiding source misidentification in the presence of strong incoherent signals. [ABSTRACT FROM AUTHOR]