In this paper, we consider a strongly repelling model of n ordered particles {e(i theta j)}(j=0)(n-1 )with the density p(theta(0), ..., theta(n-1)) = 1/Z(n )exp { - beta/2 Sigma(j not equal k )sin(-2 )(theta(j) - theta(k)/2)}, beta > 0. Let theta(j )= 2 pi j/n + x(j)/n(2) + const such that Sigma(n-1 )(j=0)x(j )= 0. Define zeta(n) (2 pi j/n) = x(j)/root n, and extend zeta(n) piecewise linearly to [0, 2 pi]. We prove the functional convergence of zeta(n)(t) to zeta(t) = root 2/beta Re (Sigma(infinity )(k=1)1/k e(ikt) Z(k)), where Z(k ) are independent identically distributed complex standard Gaussian random variables.