diff --git a/src/BlockSkylineMatrix.jl b/src/BlockSkylineMatrix.jl
index ccbc7f2..2c4edb5 100644
--- a/src/BlockSkylineMatrix.jl
+++ b/src/BlockSkylineMatrix.jl
@@ -6,7 +6,8 @@ checkbandwidths(N, M, l::AbstractVector{Int}, u::AbstractVector{Int}) =
 function bb_blockstarts(ax, l::AbstractVector{Int}, u::AbstractVector{Int})
     N,M = blocksize.(ax,1)
     L,U = maximum(l), maximum(u)
-    b_start = BandedMatrix{Int}(undef, (N, M), (L, U))
+    # zero-filled so in-band slots for blocks outside a column's own band read as 0
+    b_start = BandedMatrix(Zeros{Int}(N, M), (L, U))
     -L > U && return b_start
 
     checkbandwidths(N, M, l, u)
diff --git a/test/test_blockskyline.jl b/test/test_blockskyline.jl
index 5385648..79a3e1c 100644
--- a/test/test_blockskyline.jl
+++ b/test/test_blockskyline.jl
@@ -165,6 +165,14 @@ Random.seed!(0)
         s = split(sprint(show, "text/plain", B), '\n')[2]
         @test s == " 1  │  0  0  │  ⋅  ⋅  ⋅  │  ⋅  ⋅  ⋅  ⋅"
     end
+
+    @testset "block_starts" begin
+        # block (3,2) is in the band of block_starts but not stored, so must be 0
+        bs = BlockBandedMatrices.BlockSkylineSizes([2,3,4], [1,2,3], [2,0,0], [0,1,1])
+        @test Matrix(bs.block_starts) == [1 10  0;
+                                          3 12 20;
+                                          6  0 23]
+    end
 end
 
 end # module