We present molecular line observations of the star-forming cloud around RNO6 along with a newly discovered nearby molecular cloud that we name RNO6NW. Both clouds display striking similarities in their cometary structures and overall kinematics. By using 13CO line observations, we estimate that these clouds have similar sizes (~4.5 pc) and masses (~200 solar masses). Both molecular clouds RNO6 and RNO6NW are active in star formation. From new high resolution near-IR narrowband images, we confirm that RNO6 hosts an embedded IR cluster that includes a Herbig Be star. A conspicuous H2 filament is found to delineate the dense cometary head of the globule. RNO6NW hosts at least two IR sources and a bipolar molecular outflow of ~0.9 pc of length and ~0.5 solar masses. We show that the cometary structure of both clouds has been created by the UV radiation from numerous OB stars lying ~1.5 degree to the north. Such OB stars are associated with the double cluster h and chi Persei, and are probably members of the PerOB1 association. Thus star formation inside these clouds has been very likely triggered by the Radiation Driven Implosion (RDI) mechanism. From comparison to RDI theoretical models, we find that the similar kinematics and morphology of both clouds is well explained if they are at a re-expansion phase. Triggered sequential star formation also explains the observed spatial distribution of the members of the near-IR cluster inside the RNO6 cloud, and the morphology of the H2 filament. We conclude that the RNO6 and RNO6NW clouds are high-mass counterparts to the cometary globules of smaller masses which have been studied up to now. Thus our observations demonstrate that the RDI mechanism can produce, not only low mass stars in small globules, but also intermediate mass stars and clusters in massive clouds.