diff --git a/src/Interfaces/AbstractZonotope.jl b/src/Interfaces/AbstractZonotope.jl
index 00287cbe56..f6082b82d1 100644
--- a/src/Interfaces/AbstractZonotope.jl
+++ b/src/Interfaces/AbstractZonotope.jl
@@ -304,8 +304,8 @@ A `Zonotope`.
 
 We apply the linear map to the center and the generators.
 
-If the map has outpu dimension 1, a specialized algorithm ensures that the
-resulting zonotope only has a single generator.
+If the map has output dimension 1, a specialized algorithm ensures that the
+resulting zonotope only has a single generator (or none if the map is zero).
 """
 function linear_map(M::AbstractMatrix, Z::AbstractZonotope)
     @assert dim(Z) == size(M, 2) "a linear map of size $(size(M)) cannot be " *
@@ -326,7 +326,8 @@ function _linear_map_zonotope_1D(M::AbstractMatrix, Z::LazySet)
     @inbounds for g in generators(Z)
         gi += abs(sum(M[1, i] * g[i] for i in eachindex(g)))
     end
-    return Zonotope(c, hcat(gi))
+    G = iszero(gi) ? Matrix{N}(undef, 1, 0) : hcat(gi)
+    return Zonotope(c, G)
 end
 
 function _linear_map_zonotope_nD(M::AbstractMatrix, Z::LazySet)
diff --git a/test/Sets/Zonotope.jl b/test/Sets/Zonotope.jl
index 8aee3bec40..1fb7afc7c3 100644
--- a/test/Sets/Zonotope.jl
+++ b/test/Sets/Zonotope.jl
@@ -112,6 +112,10 @@ for N in [Float64, Rational{Int}, Float32]
     M = N[-1 1;]
     Z6 = linear_map(M, Z3)
     @test ngens(Z6) == 1 && genmat(Z6) == hcat(N[4])
+    # ... unless the map is zero
+    M = N[0 0;]
+    Z7 = linear_map(M, Z3)
+    @test ngens(Z7) == 0 && genmat(Z7) == Matrix{N}(undef, 1, 0)
 
     # in-place linear map
     Zin = convert(Zonotope, BallInf(zeros(N, 2), N(1)))