OH231.8+4.2 is a well studied O-rich CSE around an intermediate-mass evolved star that displays bipolar molecular outflows accelerated up to 400 km/s. OH231 also presents an exceptional molecular richness probably due to shock-induced chemical processes. We report the first detection in this source of HNCO, HNCS, HC3N and NO, with the IRAM-30m telescope in a sensitive mm-wavelength survey towards this target. HNCO and HNCS are also first detections in CSEs. The observed line profiles show that the emission arises in the massive central component of the envelope and at the base of the fast lobes. The NO profiles are broader than those of HNCO, HNCS, and HC3N, and most importantly, broader than the line profiles of 13CO. This indicates that the NO abundance is enhanced in the fast lobes relative to the slow, central parts. From LTE and non-LTE excitation analysis, we estimate beam-average rotational temperatures of 15-30 K (and, maybe, up to 55 K for HC3N) and fractional abundances of X(HNCO)=[0.8-1]E-7, X(HNCS)=[0.9-1]E-8, X(HC3N)=[5-7]E-9 and X(NO)=[1-2]E-6. NO is, therefore, amongst the most abundant N-bearing species in OH231. We have performed thermodynamical chemical equilibrium and chemical kinetics models to investigate the formation of these N-bearing species in OH231. The model underestimates the observed abundances for HNCO, HNCS, and HC3N by several orders of magnitude, which indicates that these molecules can hardly be products of standard UV-photon and/or cosmic-ray induced chemistry in OH231, and that other processes (e.g. shocks) play a major role in their formation. For NO, the model abundance is compatible with the observed average value. The new detections presented in this work corroborate the particularly rich chemistry of OH231, which is likely profoundly influenced by shock-induced processes, as proposed in earlier works.