  We investigate the Watts-Strogatz network with the clustering coefficient C
dependent on the rewiring probability. The network is an area of two opposite
contact processes, where nodes can be in two states, S or D. One of the
processes is governed by the Sznajd dynamics: if there are two connected nodes
in D-state, all their neighbors become D with probability p. For the opposite
process it is sufficient to have only one neighbor in state S; this transition
occurs with probability 1. The concentration of S-nodes changes abruptly at
given value of the probability p. The result is that for small p, in
clusterized networks the activation of S nodes prevails. This result is
explained by a comparison of two limit cases: the Watts-Strogatz network
without rewiring, where C=0.5, and the Bethe lattice where C=0.
