diff --git a/ChangeLog b/ChangeLog
index 03bad2c..8b9e4a6 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -49,6 +49,9 @@
    * Fixed the templates used to generate project and solution files for Visual
      Studio 2015 as well as the files themselves, to remove a build warning
      generated in Visual Studio 2015. Reported by Steve Valliere. #742
+   * Fix 1 byte buffer overflow in mpi_write_string() when the MPI number to
+     write in hexadecimal is negative and requires an odd number of digits.
+     Found and fixed by Guido Vranken.
 
 = mbed TLS 1.3.18 branch 2016-10-17
 
diff --git a/library/bignum.c b/library/bignum.c
index 4fe841c..afde19b 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -538,7 +538,12 @@
     n = mpi_msb( X );
     if( radix >=  4 ) n >>= 1;
     if( radix >= 16 ) n >>= 1;
-    n += 3;
+    /*
+     * Round up the buffer length to an even value to ensure that there is
+     * enough room for hexadecimal values that can be represented in an odd
+     * number of digits.
+     */
+    n += 3 + ( ( n + 1 ) & 1 );
 
     if( *slen < n )
     {
diff --git a/tests/suites/test_suite_mpi.data b/tests/suites/test_suite_mpi.data
index a8da378..81fc73f 100644
--- a/tests/suites/test_suite_mpi.data
+++ b/tests/suites/test_suite_mpi.data
@@ -46,6 +46,9 @@
 Test mpi_read_write_string #9 (Empty MPI -> dec)
 mpi_read_write_string:16:"":10:"0":4:0:0
 
+Test mpi_write_string #10 (Negative hex with odd number of digits)
+mpi_read_write_string:16:"-1":16:"":3:0:POLARSSL_ERR_MPI_BUFFER_TOO_SMALL
+
 Base test mpi_read_binary #1
 mpi_read_binary:"0941379d00fed1491fe15df284dfde4a142f68aa8d412023195cee66883e6290ffe703f4ea5963bf212713cee46b107c09182b5edcd955adac418bf4918e2889af48e1099d513830cec85c26ac1e158b52620e33ba8692f893efbb2f958b4424":10:"56125680981752282334141896320372489490613963693556392520816017892111350604111697682705498319512049040516698827829292076808006940873974979584527073481012636016353913462376755556720019831187364993587901952757307830896531678727717924"