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This paper investigates the problem of direction-of-arrival (DOA) estimation of rectilinear or strictly second-order noncircular signals with a partly calibrated uniform linear array (ULA). Consider that the uncalibrated portion of the array suffers from unknown gains and phases, an extended data model corresponding to a virtual (extended) array is presented by taking the noncircularity of the signals into account. On this basis and given the signal subspace matrix associated with the virtual array, a linear equation is derived to determine the unknown gains and phases. Then, the DOAs are found through the eigenvalue decomposition of a matrix related to the signal subspace matrix and array gains and phases. Since spatial spectrum search is not required, the proposed method is computationally efficient. Moreover, it is able to handle at most 2 M − 3 rectilinear signals with a partly calibrated ULA of M elements, even though only two neighboring elements of the array are calibrated. Numerical results also demonstrate that the proposed method has remarkable performance superiority brought by the rectilinearity. [ABSTRACT FROM AUTHOR]