A chaotic transition phenomenon in a five-star coupled map system resulting from recombination of synchronized clusters is analyzed numerically with the Lyapunov spectrum. When a chaotic transition phenomenon occurs, in the Lyapunov spectrum, three Lyapunov exponents take the value of nearly zero. When we introduce a locally time-averaged Lyapunov exponent, these three Lyapunov exponents fluctuate around zero. The time-variation of the difference between two of the three local Lyapunov exponents shows an intermittent behavior very similar to on-off intermittency. In the intermittent time-variation, however, the distribution function of the laminar duration time is shown as a power law with a value of power nearly equal to -2. This power law is distinguishable from that of on-off intermittency, in which the distribution function of the laminar duration time is expressed as a - 3/2 power law. Furthermore, these results are also obtained in globally coupled systems of various system sizes. We examine the results for systems with sizes of 4, 5, 8, 16, 32 and 64.