Polysomnography (PSG) has been extensively studied for sleep staging, where sleep stages are usually classified as wake, rapid-eye-movement (REM) sleep, or non-REM (NREM) sleep (including light and deep sleep). Respiratory information has been proven to correlate with autonomic nervous activity that is related to sleep stages. For example, it is known that the breathing rate and amplitude during NREM sleep, in particular during deep sleep, are steadier and more regular compared to periods of wakefulness that can be influenced by body movements, conscious control, or other external factors. However, the respiratory morphology has not been well investigated across sleep stages. We thus explore the dissimilarity of respiratory effort with respect to its signal waveform or morphology. The dissimilarity measure is computed between two respiratory effort signal segments with the same number of consecutive breaths using a uniform scaling distance. To capture the property of signal morphological dissimilarity, we propose a novel window-based feature in a framework of sleep staging. Experiments were conducted with a data set of 48 healthy subjects using a linear discriminant classifier and a ten-fold cross validation. It is revealed that this feature can help discriminate between sleep stages, but with an exception of separating wake and REM sleep. When combining the new feature with 26 existing respiratory features, we achieved a Cohen's Kappa coefficient of 0.48 for 3-stage classification (wake, REM sleep and NREM sleep) and of 0.41 for 4-stage classification (wake, REM sleep, light sleep and deep sleep), which outperform the results obtained without using this new feature.