LetF(W) be a Wiener functional defined byF(W)=I n(f) whereI n(f) denotes the multiple Wiener-Ito integral of ordern of the symmetricL 2([0, 1] n ) kernelf. We show that a necessary and sufficient condition for the existence of a continuous extension ofF, i.e. the existence of a function o(·) from the continuous functions on [0, 1] which are zero at zero to ℝ which is continuous in the supremum norms and for which o(W)=F(W) a.s, is that there exists a multimeasure μ(dt 1,...,dt n ) on [0, 1] n such thatf(t 1, ...,t n ) = μ((t 1, 1]), ..., (t n , 1]) a.e. Lebesgue on [0, 1] n . Recall that a multimeasure μ(A 1,...,A n ) is for every fixedi and every fixedA i,...,Ai-1, Ai+1,...,An a signed measure inA i and there exists multimeasures which are not measures. It is, furthermore, shown that iff(t 1,t 2, ...,t n ) = μ((t 1, 1], ..., (t n , 1]) then all the tracesf (k), $$k \leqq \left[ {\frac{n}{2}} \right]$$ off exist, eachf(k) induces ann−2k multimeasure denoted by μ(k), the following relation holds $$I_n (f) = \sum\limits_{k = 0}^{[n/2]} {\left( { - \frac{1}{2}} \right)^k \frac{{n!}}{{k!(n - 2k)!}}\int\limits_{[0,1]^{n - 2k} } {W_{t_1 } } \cdot \cdot \cdot W_{t_{n - 2k} } \cdot \mu ^{(k)} (dt_1 ,...,dt_{n - 2k} )} $$ and each of the integrals in the above expression equals the multiple Stratonovich or Ogawa type integral of the tracef(k), namely $$\int\limits_{[0, 1]^{n - 2k} } {W_{t_1 } } \cdot \cdot \cdot W_{t_{n - 2k} } \mu ^{(k)} (dt_1 , . . . , dt_{n - 2k} ) = I_{n - 2k} \circ (f^{(k)} ).$$