In this paper, we consider the component decomposition (CD) problem in a non-stationary multicomponent signal (MCS). A new technique by manipulation of morphological operations is developed to solve the CD problem. The spectrogram of the MCS is first converted into a binary image. Then, a modified opening operator is adopted to isolate the regions characterizing the individual components while suppressing the noise. The modified opening operation also compensates the energy loss caused in the binarization step. Subsequently, the regions containing the individual components are extracted using a connected-component labeling algorithm. Finally, the time-domain signals for the extracted components are reconstructed using inverse short time Fourier transform. Numerical results show that the proposed method works well for both synthetic and real data and performs better than a competing state-of-the-art method.