  We explore a local form of second-order Vasiliev equations proposed in
[arXiv:1706.03718] and obtain an explicit expression for quadratic corrections
to bosonic Fronsdal equations, generated by gauge-invariant higher-spin
currents. Our analysis is performed for general phase factor, and for the case
of parity-invariant theory we find the agreement with expressions for cubic
vertices available in the literature. This provides an additional indication
that field redefinition proposed in [arXiv:1706.03718] is the proper one.
