This paper presents a new method of estimating the direction-of-arrival (DOA) for multiple signals using minimum redundancy linear sparse subarrays (MRLSS). The proposed method makes use of the array structure to obtain the extended correlation matrix that is constructed by Kronecker Steering Vectors (KSVs) of which each contains the ambiguous and unambiguous angle with a one-to-one relationship. Our method enjoys two advantages in comparison to the existing methods. First, the cyclic ambiguity can be resolved by the one-to-one mapping of unambiguous angle without requiring additional algorithms such as MUSIC and MODE. Second, the proposed method can deal with different unambiguous angles with the same ambiguous angles, which could not have been possible by using the traditional schemes due to the fact that our method obtains the ambiguous and unambiguous angles simultaneously.