We investigated the exploratory movements of Anabantid fishes in a chessboard-like aquarium (divided into 25 communicating compartments) as a new environment. The analysis was based on the observation of the route of two inbred strains of paradise fish (Macropodus opercularis; Teleostei, Anabantoidae). We recorded their movement within the blocks until 100 steps, and compared the obtained process with hypothetical random walks. It turns out within the same period of time the fish meets significantly more new compartments than in the simulated process. The discrepancy between the two processes can be interpreted as the result of a successful exploratory strategy of the fish. In this exploratory movement the fish prefers the outer compartments to the inner ones, a fact that explains the striking difference between the actual behaviour and the "uniform simulation". This is obviously so, since the empirical data show that the transition probabilities from the actual compartment to the possible neighbouring compartments differ greatly. However, a model taking this inhomogeneity into account still does not fit sufficiently, indicating that this exploratory strategy is more complicated than our memoryless construction. Moreover, there are differences between the two strains investigated, which might reflect some role of genetic factors.