diff --git a/tree.go b/tree.go
index 394165f..23d80bc 100644
--- a/tree.go
+++ b/tree.go
@@ -13,6 +13,7 @@ package arbo
 
 import (
 	"bytes"
+	"encoding/hex"
 	"fmt"
 	"io"
 	"math"
@@ -371,6 +372,57 @@ func getPath(numLevels int, k []byte) []bool {
 	return path
 }
 
+// Update updates the value for a given existing key. If the given key does not
+// exist, returns an error.
+func (t *Tree) Update(k, v []byte) error {
+	t.updateAccessTime()
+
+	tx, err := t.db.NewTx()
+	if err != nil {
+		return err
+	}
+
+	keyPath := make([]byte, t.hashFunction.Len())
+	copy(keyPath[:], k)
+	path := getPath(t.maxLevels, keyPath)
+
+	var siblings [][]byte
+	_, valueAtBottom, siblings, err := t.down(tx, k, t.root, siblings, path, 0, true)
+	if err != nil {
+		return err
+	}
+	oldKey, _ := readLeafValue(valueAtBottom)
+	if !bytes.Equal(oldKey, k) {
+		return fmt.Errorf("key %s does not exist", hex.EncodeToString(k))
+	}
+
+	leafKey, leafValue, err := newLeafValue(t.hashFunction, k, v)
+	if err != nil {
+		return err
+	}
+
+	if err := tx.Put(leafKey, leafValue); err != nil {
+		return err
+	}
+
+	// go up to the root
+	if len(siblings) == 0 {
+		t.root = leafKey
+		return tx.Commit()
+	}
+	root, err := t.up(tx, leafKey, siblings, path, len(siblings)-1)
+	if err != nil {
+		return err
+	}
+
+	t.root = root
+	// store root to db
+	if err := tx.Put(dbKeyRoot, t.root); err != nil {
+		return err
+	}
+	return tx.Commit()
+}
+
 // GenProof generates a MerkleTree proof for the given key. If the key exists in
 // the Tree, the proof will be of existence, if the key does not exist in the
 // tree, the proof will be of non-existence.
diff --git a/tree_test.go b/tree_test.go
index 7444836..bb67954 100644
--- a/tree_test.go
+++ b/tree_test.go
@@ -104,8 +104,8 @@ func TestAddDifferentOrder(t *testing.T) {
 	defer tree1.db.Close()
 
 	for i := 0; i < 16; i++ {
-		k := SwapEndianness(big.NewInt(int64(i)).Bytes())
-		v := SwapEndianness(big.NewInt(0).Bytes())
+		k := BigIntToBytes(big.NewInt(int64(i)))
+		v := BigIntToBytes(big.NewInt(0))
 		if err := tree1.Add(k, v); err != nil {
 			t.Fatal(err)
 		}
@@ -116,8 +116,8 @@ func TestAddDifferentOrder(t *testing.T) {
 	defer tree2.db.Close()
 
 	for i := 16 - 1; i >= 0; i-- {
-		k := big.NewInt(int64(i)).Bytes()
-		v := big.NewInt(0).Bytes()
+		k := BigIntToBytes(big.NewInt(int64(i)))
+		v := BigIntToBytes(big.NewInt(0))
 		if err := tree2.Add(k, v); err != nil {
 			t.Fatal(err)
 		}
@@ -134,8 +134,8 @@ func TestAddRepeatedIndex(t *testing.T) {
 	c.Assert(err, qt.IsNil)
 	defer tree.db.Close()
 
-	k := big.NewInt(int64(3)).Bytes()
-	v := big.NewInt(int64(12)).Bytes()
+	k := BigIntToBytes(big.NewInt(int64(3)))
+	v := BigIntToBytes(big.NewInt(int64(12)))
 	if err := tree.Add(k, v); err != nil {
 		t.Fatal(err)
 	}
@@ -144,6 +144,56 @@ func TestAddRepeatedIndex(t *testing.T) {
 	c.Check(err, qt.ErrorMatches, "max virtual level 100")
 }
 
+func TestUpdate(t *testing.T) {
+	c := qt.New(t)
+	tree, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon)
+	c.Assert(err, qt.IsNil)
+	defer tree.db.Close()
+
+	k := BigIntToBytes(big.NewInt(int64(20)))
+	v := BigIntToBytes(big.NewInt(int64(12)))
+	if err := tree.Add(k, v); err != nil {
+		t.Fatal(err)
+	}
+
+	v = BigIntToBytes(big.NewInt(int64(11)))
+	err = tree.Update(k, v)
+	c.Assert(err, qt.IsNil)
+
+	gettedKey, gettedValue, err := tree.Get(k)
+	c.Assert(err, qt.IsNil)
+	c.Check(gettedKey, qt.DeepEquals, k)
+	c.Check(gettedValue, qt.DeepEquals, v)
+
+	// add more leafs to the tree to do another test
+	for i := 0; i < 16; i++ {
+		k := BigIntToBytes(big.NewInt(int64(i)))
+		v := BigIntToBytes(big.NewInt(int64(i * 2)))
+		if err := tree.Add(k, v); err != nil {
+			t.Fatal(err)
+		}
+	}
+
+	k = BigIntToBytes(big.NewInt(int64(3)))
+	v = BigIntToBytes(big.NewInt(int64(11)))
+	// check that before the Update, value for 3 is !=11
+	gettedKey, gettedValue, err = tree.Get(k)
+	c.Assert(err, qt.IsNil)
+	c.Check(gettedKey, qt.DeepEquals, k)
+	c.Check(gettedValue, qt.Not(qt.DeepEquals), v)
+	c.Check(gettedValue, qt.DeepEquals, BigIntToBytes(big.NewInt(6)))
+
+	err = tree.Update(k, v)
+	c.Assert(err, qt.IsNil)
+
+	// check that after Update, the value for 3 is ==11
+	gettedKey, gettedValue, err = tree.Get(k)
+	c.Assert(err, qt.IsNil)
+	c.Check(gettedKey, qt.DeepEquals, k)
+	c.Check(gettedValue, qt.DeepEquals, v)
+	c.Check(gettedValue, qt.DeepEquals, BigIntToBytes(big.NewInt(11)))
+}
+
 func TestAux(t *testing.T) {
 	c := qt.New(t)
 	tree, err := NewTree(memory.NewMemoryStorage(), 100, HashFunctionPoseidon)