  The connection is obtained between Ward identities and W-constraints in
Generalized Kontsevich Model with the potential $X^4/4$. We show that Ward
identities include W-constraints (and do not include any other constraints) for
this potential and make some observations in favour of the same connection for
the model with the potential of the form $X^{(K+1)}/(K+1)$ for any $K\geq 2$.
