By using a source method and improved measuring techniques, we study the decay of the Polyakov loop in SU(3) lattice gauge theory at finite temperature. Our aim is to measure the correlation length of the system in the neighbourhood of the critical point. We work with lattices of size up to 162×64×4. We found that the maximum correlation length is only bounded by the spatial dimension of the lattice. This result is the one expected in a second order phase transition and appears to be incompatible with the presence of the strong first order transition claimed in the literature.