  We develop an approach to constructing the manifestly Lorentz covariant cubic
interaction vertices for the four-dimensional massless higher spin bosonic
fields with two-component dotted and undotted spinor indices. Such fields
automatically satisfy the traceless conditions what simplify form of the
equations determining the irreducible massless representation of the Poincar'e
group with given helicity. The cubic vertex is formulated in the framework of
the BRST approach to higher spin field theory. Use of the above spin-tensor
fields allows to simplify a form of the BRST-charge and hence to find the cubic
vertices just in terms of irreducible higher spin fields. We derive an equation
for the cubic vertex and find solutions for arbitrary spins $s_1,s_2,s_3$ with
the number of derivatives $s_1+s_2+s_3$ in the vertex. As an example, we
explicitly construct a vertex corresponding to the interaction of a higher spin
field with scalars.
