diff --git a/docs/src/index.md b/docs/src/index.md
index 2100fb2..f2c44e6 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -87,6 +87,7 @@ ADTypes.AbstractColoringAlgorithm
 ADTypes.column_coloring
 ADTypes.row_coloring
 ADTypes.symmetric_coloring
+ADTypes.bicoloring
 ADTypes.NoColoringAlgorithm
 ```
 
diff --git a/src/ADTypes.jl b/src/ADTypes.jl
index 0a1f66d..9558eb2 100644
--- a/src/ADTypes.jl
+++ b/src/ADTypes.jl
@@ -68,7 +68,7 @@ export jacobian_sparsity, hessian_sparsity
 
 # Matrix coloring
 export AbstractColoringAlgorithm
-export column_coloring, row_coloring, symmetric_coloring
+export column_coloring, row_coloring, symmetric_coloring, bicoloring
 @public coloring_algorithm
 @public NoColoringAlgorithm
 
diff --git a/src/sparse.jl b/src/sparse.jl
index 953c334..80beb63 100644
--- a/src/sparse.jl
+++ b/src/sparse.jl
@@ -115,6 +115,7 @@ Abstract supertype for Jacobian/Hessian coloring algorithms.
   - [`column_coloring`](@ref)
   - [`row_coloring`](@ref)
   - [`symmetric_coloring`](@ref)
+  - [`bicoloring`](@ref)
 
 # Note
 
@@ -154,6 +155,23 @@ The result is a coloring vector `c` of length `size(M, 1) == size(M, 2)` such th
 """
 function symmetric_coloring end
 
+"""
+    bicoloring(M::AbstractMatrix, ca::ColoringAlgorithm)::Tuple{AbstractVector{<:Integer},AbstractVector{<:Integer}}
+
+Use algorithm `ca` to construct a structurally orthogonal partition of both the rows and columns of the matrix `M`, ensuring no two non-zero entries in the same row or column share the same color.
+
+The result is a tuple of coloring vectors `(cr, cc)` of lengths `size(M, 1)` and `size(M, 2)`, respectively.
+The vector `cr` provides a color assignment for each row, and `cc` provides a color assignment for each column.
+For each non-zero entry `M[i, j]` in `M`, at least one of the following conditions holds:
+
+  - row `i` is the only row with color `cr[i]` that has a non-zero entry in column `j`;
+  - column `j` is the only column with color `cc[j]` that has a non-zero entry in row `i`.
+
+A neutral color `0` may be assigned to rows or columns, indicating that they are not needed to retrieve all non-zero entries in `M`.
+This occurs when the entries in a row (or column) are fully determined by the non-zero entries in the columns (or rows).
+"""
+function bicoloring end
+
 """
     NoColoringAlgorithm <: AbstractColoringAlgorithm
 
@@ -168,6 +186,7 @@ struct NoColoringAlgorithm <: AbstractColoringAlgorithm end
 column_coloring(M::AbstractMatrix, ::NoColoringAlgorithm) = 1:size(M, 2)
 row_coloring(M::AbstractMatrix, ::NoColoringAlgorithm) = 1:size(M, 1)
 symmetric_coloring(M::AbstractMatrix, ::NoColoringAlgorithm) = 1:size(M, 1)
+bicoloring(M::AbstractMatrix, ::NoColoringAlgorithm) = 1:size(M, 1), 1:size(M, 2)
 
 ## Sparse backend
 
diff --git a/test/runtests.jl b/test/runtests.jl
index 2e3f3e7..00887a3 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -16,7 +16,8 @@ using ADTypes: dense_ad,
                coloring_algorithm,
                column_coloring,
                row_coloring,
-               symmetric_coloring
+               symmetric_coloring,
+               bicoloring
 using Aqua: Aqua
 using ChainRulesCore: ChainRulesCore, RuleConfig,
                       HasForwardsMode, HasReverseMode,
diff --git a/test/sparse.jl b/test/sparse.jl
index 10c1c01..31d7b1a 100644
--- a/test/sparse.jl
+++ b/test/sparse.jl
@@ -159,4 +159,13 @@ end
     @test sv isa AbstractVector{<:Integer}
     @test length(sv) == size(M, 1) == size(M, 2)
     @test allunique(sv)
+
+    M = rand(3, 4)
+    brv, bcv = bicoloring(M, ca)
+    @test brv isa AbstractVector{<:Integer}
+    @test bcv isa AbstractVector{<:Integer}
+    @test length(brv) == size(M, 1)
+    @test length(bcv) == size(M, 2)
+    @test allunique(brv)
+    @test allunique(bcv)
 end