  We perform Monte Carlo simulations of a gauge invariant spin system which
describes random surfaces with gonihedric action in four dimensions. The
Hamiltonian is a mixture of one-plaquette and additional two- and
three-plaquette interaction terms with specially adjusted coupling constants.
For the system with the large self-intersection coupling constant $k$ we
observe the second-order phase transition at temperature $\beta_{c}\simeq
1.75$. The string tension is generated by quantum fluctuations as it was
expected theoretically. This result suggests the existence of a noncritical
string in four dimensions. For smaller values of $k$ the system undergoes the
first order phase transition and for $k$ close to zero exhibits a smooth
crossover.
